Paris and London 9 days itinerary help!

Go to http://www.eurostar.com/us-en to search for Eurostar tickets. Many of the trains during your time period have their cheapest fares sold out, but there are many others with reasonable fares still available. The site makes it easy for you to compare fares across different days and different times.

In choosing a time, remember that you will need to be at the station at least 30-45 minutes before departure to go through check-in and security.

London is a large city with varied neighborhoods and numerous hotels, no single one of which is best for everyone, so it would help to know a little about your criteria. What is your budget per night, or what standard of accommodation are you looking for? Would you prefer to be in a tourist-focused area or a quieter (by London standards) residential neighborhood?

I take it you want to spend part of your 9 nights in London, and the rest in Paris.
If it isn't too late, try booking an "open jaw" ticket, into Paris and out of London (or vice-versa). That would save doubling back.

Do not travel Paris to London (or vice-versa) on the same day you fly. You would have to build in too much contingency between the two methods of travel, and waste too much time travelling.

Best time and date is up to you. There are trains approx every hour, and it takes ~2 hours 20 mins, so whenever you want.
Look up times and book on http://www.eurostar.com/ The earlier you book, the cheaper the fare. I would book ASAP (today), before the fares go up even more. For example, 28th May, Paris to London, is currently selling at from £58 per person.

Our budget is flexible ($100-200/night) and we have stayed in the 6th and 7th of Paris, (6th being quieter and we preferred). We do plan on walking and possibly taking a few walking tours while in London. We would like to stay someplace where walking is not a problem. The Eurostar to London was an after thought, so changing the tickets to open-jaw is a bit too late. Like is said, not ideal travel plans, but doable knowing we have spent time in Paris previously.

I'd spend as much time as possible in London. It's a great city with tons and tons of things to see and do, plus too many day trips to fit into a week.

London sights are more spread out than in Paris. No area is perfect. Like Paris, being near the tube is more important, and being near a station with more lines is better.

Best Eurostar - whatever's cheapest. You can get to/from St. Pancras and Nord anytime. If you are taking a taxi to your London hotel, a late arrival means a lot less city traffic.

As for itinerary for London, it depends upon what your interests are. Public transportation is excellent - the tube and buses make getting around London easy. In my experience (10 trips and counting!) I've stayed in a variety of areas and each has it's charms. Nowadays I'm partial to the Earls Court area but given how good the public transport is, no one area in central london is better or worse than another, location wise.
So here are some suggestions for what they are worth:

Pick up or borrow Rick Steves guide on London. Just about everything you need to know to craft an itinerary is covered.

Once you've got a list and an idea of what you want to see/do, lots of folks here can advise and help you refine your itinerary.

As for places to stay can't really advise on hotels since we generally either rent an apartment (airbnb or vrbo) or stay in an aparthotel. (Fraser Suites and Citadines are two that we've stayed at). Advantage is that each room comes with a small kitchenette which is handy for breakfast, snacks and dinner in - M and S Simply Food, Waitrose, etc, etc. have pretty decent "heat and eat" meals which can help with the budget!!!

Things to do that you might consider:
-London walks - great walking "tours" of London. Fabulous way to see parts of London you might never see! There is an extensive list of walks listed on their website - best part is no reservation required. Simply show up at the appointed time and place. We've done about 25 of them and have thoroughly enjoyed every one!
-Evensong at Westminster Abbey - even if you aren't religious, this is roughly 45 minute service (which is mostly sung!) is a great way to experience the Abbey.
-If you are there on a Saturday, head over the Brick Lane - fun market with tons of food stalls selling foods from every corner of the globe.

Happy planning!!!