Okay..that clarification is very useful. I wasn't sure if this was a party of a mother and three teenage girls or four adults.
In Paris (which is the city I really know) you have a very wide range of rooms and prices. For people looking to keep costs down I always recommend the Hotel St. Andre Des Artes which is where I stay. They have a quad room that goes for 120 euros a night (breakfast included). But I must say that this is NOT the Holiday Inn. Its clean and has modern plumbing but there's no elevator, no mini bars and no TV. Its very French tho and I think its charming (I've been staying there for more than 30 years). You can book thru their webpage: http://www.france-hotel-guide.com/h75006saintandredesarts.htm
London hotels are expensive these days. I like the Arran House Hotel in Bloomsbury. They have a quad with en suite facilites for £117. The price does includes a full English breakfast and that will fill you up a treat so the price is not too bad.. Their website is here: http://www.arranhotel-london.com/newsletter_0307.htm
What to see and do in London
The changing of the guard in London is something most Tourists enjoy. There is also a changing of the Horse Guards which, I think, is even better. (They wear brass helmets and partial armor and carry sabers...really rather nifty looking).
You can only see Buckingham Palace from the outside. there are no guided tours like they have of the White House. There used to be a rather clever way of getting inside known to only a few. You could go to the side entrance of the Palace dressed very nicely and ask to sign the Queen's guest book and would then be escorted inside to do so. I understand this has been discontinued in light of present day security concerns.
Getting around London on the Underground or the busses isn't all that hard although its become a lot more expensive than it used to be. (But then everything is way more expensive than when I first went to London as a child).
As to what to do in London there is a rather long list but the basics are:
1) Tower of London...The Beefeaters (The Yeoman of the Guard) give wonderful tours. Well worth it to see the crown jewels, Traitors Gate, the place where Anne Boleyn was beheaded and such.
2) St. Paul's Cathedral Sir Christopher Wren's masterpiece. he's buried there with the incription "Lector, si monumentum requiris, circumspice" (Reader, if you seek a monument, look around you)
3) Westminster Abbey .. The burial place of many of England's most fanmous men and the site of Britain's Tomb of the Unknown Soldier. The inscription which end's with these words always brings tears to my eyes:
"They buried him among the kings
Because he
Had done good toward God and
Toward His house"
4) Houses of Parliament. Visiting Parliament is possible and you can attend a session. Its easier to visit the House of Lords as the lines are not usually so long.
5) See a West End play. The London theatre scene is excellant. dson't miss seeing a play while there.
6) Trafalgar Square/ Piccadily Circus.. Yes its terribly touristy but why not.
7) Greenwich..Take the boat ride up the Thames and see, among other things, the Royal Observatory.
8) Go shopping at Harrod's ... Even if you don't buy anything check out the Food courts..they are astounding
Driving in the UK can be quite difficult...recall they drive on the other side of the road. And you'll find that most British roads just don't compare to those in the USA. But, if you're heading off the beaten path you may have no practical choice.
What to see and do in Paris
As for what to see in Paris I've just written a rather long itinerary for a four stay stay for some other folks which would apply equally to your needs. its here https://answersrip.com/question/index?qid=20070328011253AASjWN0
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