London and Paris

Having only 4 days in London, I would focus on London and skip Stonehenge.
But if you very much want to go to Stonehenge while staying in London, you could use one of these organized daily trips that cover Windsor, Bath and Stonehenge or just two places. Yes, it is a bit rushed, but at least you've got a lot covered.
Like this one:
http://www.goldentours.com/windsor-bath-and-stonehenge

Budget?

Which 3/4 star amenities do you need or prefer? Are you aware that in Europe the number of official stars is based on facilities and amenities at the hotel and has nothing directly to do with quality or comfort nor customer experience?

This seems like still quite a rush, but much longer and more focussed than you originally planned.

A day trip that covers Windsor, Stonehenge and Bath in a single day is not recommended by most Brits, as you will spend too long in transit sat on a motorway and little time actually seeing things.

Stonehenge is reached by getting a train to Salisbury, then getting a bus to the monument. It means that you can't get there early enough to pick up the quieter early entry unless you stay there the night before. I would suggest with only 4 days in London that you leave Stonehenge for another visit.

@ Jennifer, you are very right, a lot of time is actually spent in transit and it is really annoying you cannot enjoy things properly.
So having heard that, I had serious doubts deciding for such option, but at the end I took it and I am very pleased to have seen all those places.
But yes, we certainly agree it is better just to stay 4 days in London especially for first timers.

Lesley ,
In july the days will be long so what we do when we're in London is make sure we do all the sights that close earlier and see the sights that are in a certain area. I always stay right around Victoria Station as you save so much time going to so many places or connecting. Kensington is not far , Westminster Abby , Buckingham Palace , Changing of the Guards . We had a ten minute walk with a Starbucks on the way to the station. There are all kinds of places from B&B to smaller English hotels so check it out. Ian Fleming , Margaret Thatcher lived one block or two from Ebury St in Belgravia area. , "where we stay " and Babs too has or had a place in the same area. We went into a Chocolate shop one evening and the girl waiting on us said Sean Connery had just left " William Curley – 198 Ebury Street Belgravia" . One of the oldest.
Go to the Tower of London , Westminster Abby " have to do that " and don't forget the museum's are FREE . When the places are closed for the day then since you'll have hours of daylight left so take a London Walk in the evening. Cost maybe 6 or so pounds maybe .. not sure as each one might be different. Lots of places to choose from "we did Jack the Ripper Walk " and it was great. Their is a Pub walk where you eat , another goes to the oldest parts of London so many that I can't remember. There is even one that a guide is with you going to Stonehenge. Every time I go to London I take one ," a friend of mine goes along who is a Londoner " she enjoyed it and saw places she had not been to !
Also eat at pubs , they have great food and you'll get to meet the locals. Get your drinks "soda " too at the bar it's cheaper then being waited on. They were so good to us , "since you American's like ice here is some extra ", they did it without us asking ! I have had Cabbies refuse a tip , you don't have to give a lot like we do here. They study for years passing tests to become one "have to know every street in London " some have the same name too. Interesting to check out their website.
I know I have left a long trail of advice but each time I go , picked up something that I wish I had known on my first visit..
ps. if you want to go to Stonehenge GO , it is one place you have to see in person to appreciate it.

Emma recommends a location close to the Tube's dark blue Piccadilly Line, and I tend to agree.
A selection of four stars ...
Knightsbridge - http://www.thelevinhotel.co.uk/
Green Park - http://www.chesterfieldmayfair.com/
Piccadilly/Leicester Sq - http://www.every-hotels.com/hotels/united_kingdom/london/every_piccadilly/
Holborn - https://thehoxton.com/london/holborn

I have done a bus tour to Stonehenge.. that included Bath and Salisbury
It was my second visit to Bath( did it on my own once before )

The bus tour gave enough time for Stonehenge.. and Salisbury.. but not enough for Bath.. but then that is my perspective. It certainly is the easiest way to see all three/. and frankly , I do not think Stontehenge is worth the trip just for it....

In Paris look for hotels in 4 , 5th and 6th. You can put in your info into booking.com.. and your price range etc.. and check out their selections. You can the check hotels own website and see which offers best price.
Do you need one room ( are children very young?) or two. Hotel rooms WILL be smaller then you expect.

Lesley, I'll go with the faction that recommends skipping Stonehenge. London is a vast city with far, far more to cover than you can begin to manage in four days so I'd spend all of your time there.

Emma is spot on that nowhere in London will be close to ALL of its larger attractions but she is also right that nothing is that far away by public transport. We really liked the South Kensington area as it was close to Hyde Park, Kensington Palace, the V&A and some other interesting places to explore but close to tube stations for hops farther afield. We also just walked to Westminster, Buckingham, Green and James Parks, Chelsea and any number of other places around the city from there.

Nigel is also spot on that hotel stars in Europe are not issued by guest ratings but by the amount of amenities a property provides. You may be perfectly comfortable in a two or three-star property if the location and minimal amount of must-haves fill the bill.

Does four days in London really mean one day of arrival, two days there, and then on the fourth day you depart for Paris? That means two full days and parts of two days (including your arrival jet lag day). Or is the departure for Paris a day later so you have three full days and parts of two days?

Same for Paris - is one day arrival day and one day departure day? I.e. two full days plus the day you arrive (the day you depart, you'll do nothing but go to the airport).

Wondering if you have four days in each city or fewer.

We had an excellent experience staying at the Hotel Relais Bosquet in Paris last summer. We were able to walk to many of our "must sees" and public transport was convenient. If you like their Facebook page there is a special discounted rate that includes an amazing breakfast.

Paris Hotel Relais Bosquet is great! I think 3 stars, but since we usually rent apartments or stay in small B&Bs, it was luxury to us!

If you truly have 4 days to explore London (and not 2 as one post wonders), and even if you've never been to London and all its attractions before, and even if you reasonably expect to return....let me weigh in on the side of doing a coach bus daytrip to Windsor Castle/Bath/Stonehenge. I've done 4 of these with EvanEvans and they are a good way to see distant sites. And this one was by far my favorite (one was a daytrip to Paris).

"A day trip that covers Windsor, Stonehenge and Bath in a single day is not recommended by most Brits, as you will spend too long in transit sat on a motorway and little time actually seeing things."

I'm not a Brit, but concur wholeheartedly with this :-) My family and I did the Bath/Lacock/Stonehenge tour (booked through Premium tours) back in late March 2015, and it was a long, LOOOONNNGG day ... and yes, most of it sitting on a bus :-/ Bath was "okay, kind of interesting," but not mind-blowing; all we really did in Lacock was have dinner (which was excellent); and Stonehenge was a great experience but not quite as awe-inspiring as I'd expected ... but that may have been due in part to the cold, rainy weather, which just made me long to be back on the bus :-D

In retrospect, I wish we hadn't lost an entire day doing the Stonehenge trip; we had only three days in London, and it was nowhere near enough :-(

I can add my vote to Hotel Relais Bosquet. I stayed there for a week in October and it was wonderful. The room was very large by Euro standards, and extremely comfortable, the breakfast was lavish, and the staff more than helpful. Right around the corner from the Rue Cler and all its cafes and food shops. A quick walk to the Metro and also a lovely walk to the Eiffel Tower and the Champ du Mars. I'm looking forward to returning there to stay again in the fall this year.

Hint, if you book via their Facebook page breakfast will be included in your room rate.