First timer

You really need to get moving on finding accommodations. The rest of your trip will come together.
I'd suggest you get a good travel guide at either a bookstore or library and figure out which neighborhoods you want to stay in.
Then go on AirBnB.com or Booking.com and find a place to stay in those locations.

Ms Sharp, if you leave in only 10 days (now 9 days) please, please book a hotel room this very minute. Forget Air what's its name, you have left it too late to find an acceptable, vettable, legitimate AirB&B place.

Not knowing someone who has been to London or Paris is not a problem. You do know about Rick Steves so get his London and Paris guide books and read, read, read. For Paris check out tomsguidetoparis.com and parisbytrain.com.

It is overwhelming, but you have time to get less whelmed, and get that hotel room asap.

You will find accommodation recommendations in Rick's guide books as well as on the review boards on this forum. I would start with Booking.com and start searching using your nightly budget and the map function to locate suitable lodging. TripAdvisor.com is another good source for reviews and to book lodging.

As for things to do in each city, the guidebooks are very useful as well. Other useful resources are on this website. For London, check this link and explore the sites and determine what interests you the most:
https://www.ricksteves.com/europe/england/london

Same for Paris:
https://www.ricksteves.com/europe/france/paris

If you plan to go to many museums in Paris, look into the Paris Museum Pass. It offers admission to most of the top museums in Paris and allows you to skip the ticket line. I would not buy that in the states. I would go to one of the museums in Paris and buy it there. With your schedule, you might consider the 2 day pass.
http://en.parismuseumpass.com/

I'll agree with the rest: you need to book your accommodations ASAP.

I can't weigh in on the London Pass but can tell you that there are a great many things to see in the city including some excellent museums which are free. We spent a week in the city some years back and merely scratched the surface. Along with a good guidebook, you'll find lots of info on the London Pass website.

Paris: you might take a look at a 2-day Paris Museum Pass (NOT the Paris Pass). As with any other pass, you have to add up the individual entry fees of the attractions you know you'll be visiting to see if the pass is worth the price. Personally, I wouldn't have planned on using a hoho bus as your method of transport around the city but so be it. Anyway, that pass (we had the 6-day as we had a week in the city) was a good buy for us. It does not need to be purchased in advance: buy it when you get to Paris. It does not cover use of public transport.

Without having your exact dates for Paris, you may need to plan your two full days of sightseeing on a pass around days certain of the museums are closed (e.g. Louvre on Tuesdays, d'Orsay on Monday's, etc.) If possible, take advantage of evenings that some of them are open late to maximize the number of attractions you could visit with the pass.

http://en.parismuseumpass.com

You are going to have difficulties finding good value accommodation at this late stage. Look at the Premier Inn or Travelodge chains in London. Booking.com is another good option. Avoid Airbnb - too late for this and not the best option for London.

It's no use telling you that the London Pass isn't good value, as you have already bought it!

I agree with the others that you want to book your accommodations ASAP, and that your best route is to go for a traditional hotel rather than AirBnB. However, there is no need to panic. A quick search of booking.com shows that there are hundreds of London hotels with available rooms on your dates. You'll have the best selection if your budget allows for upwards of $200 per night. (But note that unlike in the US, UK hotel prices are typically listed with all taxes included, so the price you see is the price you'll pay.)

Your Eurostar tickets entitle you to two-for-one admission into certain museums. Because your tickets originate in London, you'll be eligible for the Paris offers here: http://www.eurostar.com/us-en/deals/2for1?intcmp_hp_pos5_B_2for1

It's hard to say what is not to miss for London without knowing your interests. There is so much to do. You seem to have reasonable length of stay for London so that is in your favor. I suggest checking the Victoria/Pimlico area for reasonably priced hotels.

I really enjoyed Tower of London, Hampton Court Place, a walk in Hyde Park and just spending time strolling around the city. I think a don't miss would be taking a day trip outside of the city to a more rural area or another city. Maybe take a day trip to Dover Castle or Bath or some other place that strikes your fancy. Just get out of London for at least one day trip.

Taking a day trip to Eastbourne for a short hike along the cliffs and catching a play with some big name actors in it (and meeting them the stage door afterwards) were highlights of my (5 day) trip.

One thing we didn't get to do that I would have liked to have done was have a traditional afternoon tea. We also didn't go on the London Walks walking tour we had planned because we didn't schedule it early enough in our trip. We were so work out by touring around each day that by the time we had an opportunity to go on a walk the thought of more walking didn't appeal.

Whatever you do you should have a fabulous time.

Thank you so much for the information. I am curious why everyone is recommending that we avoid AirBnB? We used it in Oslo and the apartment was awesome. We are vegetarians and have other diet restrictions so even in the states we do most of our cooking at home. Which is why we want a kitchen and are avoiding hotels. We also want to pack light so with only a few articles of clothing we really appreciate having a washer and dryer. I have many guidebooks, but there are TOO many things to choose from. Is there ANYTHING we really should buy here in the states BEFORE arriving? I don't want to purchase anything else pre-trip unless I have to. And it may be inconvenient but since we are trying to get last minute accommodations is staying in the suburbs out of the question for London and/or Paris? (We could rent a car while in Paris. ?????) I am booking SOMETHING today. :) Thank you in advance for your help.

There have been a number of threads on this site where people have been looking into AirBnB-type accommodations in London that turned out not to be as advertised (e.g., in a dodgy neighborhood instead of a cool one). If you don't know the city well, it can be hard to spot things like that. A traditional hotel, in my opinion, gives you a better chance of getting what you paid for. Sites like booking.com let you search for just those with kitchen and laundry facilities, if that's important to you.

London is one of the best cities (and the UK is one of the best countries) in the world for vegetarians (though I can't speak to your other restrictions, not knowing what they are). I'm a vegetarian too, and I've never had any trouble keeping myself fed in London or anywhere in the UK.

As for things to buy: Do you have electrical plug adapters? The UK and France use different-shaped plugs from the US (and from each other). You can buy them at the airport or after you land, but if you think you might be in a situation where you have to charge your gadgets right away, it's helpful to have them already.

Thank you for your quick reply KH Buzzard. I've been on Booking.com and found some beautiful apartments with kitchens and washing machines, in the heart of London. PERFECT for us! I thought the only way to get an apartment was through AiBnB or some-such. Now to pick one before they are all gone!! Decisions. Decisions! Thanks again!

Any comments on Barbican neighborhood? Thanks.

I was going to suggest an apartment but it looks like you found them. I saw a bunch when I was booking our trip and they were reasonably priced and appeared to be in good neighborhoods. I would stay in the city if you can. It will cut down on travel time but London's rail/tube system is great if you can't find something close in.

London has everything so I don't know why you would need to purchase anything before you leaved if you don't want to. Just make sure you have any prescription medications you might need. Or if you use a clinical strength deodorant. Otherwise you can get it there. I had to purchase cold medications while there and found their cold medications to be better than American medications.

I can't comment on Paris.

I would not stay in suburbs of either city -- takes too long to get in and out for sightseeing, and it can be nice to return to your hotel or apartment in the middle of the day and then get out there again. You might save money but your time is valuable too. (That said, Islington isn't too far out, in response to your other thread.)

Apart from your passport, credit/debit cards, and any meds, I can't think of anything you absolutely must bring from home (though it's convenient to have some clothes, I guess). BTW be sure to let your credit card issuer and bank know about your travel plans so they won't cancel your cards when you use them overseas.

The Paris Museum Pass can be a good value, and a time-saver, but you'll be there so short a time it may not be worthwhile. No need to buy it before your trip though.

Any comments on Barbican neighborhood? Thanks.

Yes. It's an interesting fairly central area, near St Paul's Cathedral and on the fringes of the City (the traditional business district) but also not that far from many tourist sites as well.

Is the flat on the Barbican Estate? It is a big 1960s development that is architecturally distinguished and the flats go for hundreds of thousands if not millions, although if it were anywhere other than central London it might look a bit scary - lots of pedestrian passageways and dark overhangs, but it's very safe and there's a big arts centre as part of the complex.

You asked if there was anything you should buy HERE before leaving: while I usually take enough small packaged sundry items (toothpaste etc.) because I don't want to rush around to find a store immediately, I don't worry if I have to buy them. BUT the one thing I take enough of for the entire trip is contact solution (sharing in case you wear contacts). I am allergic to some versions, and since you don't see the same brands in Europe, I want to make sure I have enough of my regular solution. Otherwise, buy what you may need there; it's part of the adventure.

I like the Barbican area. One of my favorite museums is located there; The Museum of London.
Walk south from the Barbican area, and you are at St. Paul's Cathedral. Across the street (to the south) from St. Paul's is the Tourist Information Centre. They can answer a lot of your questions you may have, and will give you bus route and tube maps.

A major handy bus line runs on the street that is between St. Paul's and the T.I. Centre. The number 15 bus line runs east and west and will take you from St. Paul's (east) to the Tower of London, a must-see for London, in my opinion. If you get on the number 15 bus at St. Paul's headed west, it will take you to Trafalgar Square.

You asked if there is anything else you should buy before leaving for your trip.
I suggest you go to your nearest bookstore and buy the Rick Steves Pocket London guidebook, shown here:
https://store.ricksteves.com/shop/p/pocket-london
It is small, weighs practically nothing, and has a fold out map of London, which you will need.
If you don't want to buy the pocket guidebook, at least buy a very good map of London. You'll be lost without it.

You may want Rick's Paris Pocket guide also:
https://store.ricksteves.com/shop/p/pocket-paris
Has a fold-out map.

There are so many must-sees in London and Paris that it really depends on your interests. Some top London area attractions are Big Ben, Westminster Abbey, the London Eye, Buckingham Palace, Windsor, Hampton Court, The Shard, Tower of London, Tower Bridge, any of the Markets, the museums. We really enjoyed everything we did, but in particular Camden Market, Westminster Abbey, and Hampton Court. There are many great day trips from London too. We did a Bath/Cotswolds/Stonehenge day tour, and while it was a pretty full day, we enjoyed getting a few hours in each of those places. We particularly loved Bath, so much so that we considered doing a full day trip there on our upcoming trip next month. We decided on York instead for this time, but I don't think you could go wrong with Bath if you're looking to get out of London for a day. It's a very beautiful city.

In Paris, some of the top attractions are the Eiffel Tower, the Louvre, the D'Orsay, Notre Dame, Sainte Chapelle, Arc de Triumphe and Champs Elysses, the Catacombs, Père Lachaise cemetery, Latin Quarter, Jardins de Luxembourg, Place des Vosges, day trip to Versailles, and probably many more I'm not thinking of.

What are your interests? That would help us narrow down specific attractions that you shouldn't miss.

You ask whether you should rent a car in Paris: absolutely not! The metro and buses are wonderful and easy - plus, didn't you say you'd already booked a 2-day bus tour? For 2 or 3 nights only in Paris, definitely go with a hotel, or an aparthotel, like Citadines.

I agree with Shelly - do NOT rent a car in Paris. Traffic is dreadful, parking expensive and there's no need for a car as Paris has an excellent Metro / RER / Bus network so there's absolutely no need for a car. Also keep in mind that each driver registered on the rental form will require either an International Driver's Permit, which is used in conjunction with your home D.L. OR a certified translation of the terms of your home D.L. in French.

Oy. No. Do not rent a car in Paris! Stay in the centre where all the things you want to see are located and public transit is excellent.

(My comment is for anyone reading this thread for their own research as the OP has booked their accommodations.)