Two Weeks in London and Paris

Museums are free in London. Kids under 16 (I think) travel quite cheaply in London, and under 11 travel free with an adult. I'm a fan of the all day bus pass because it's cheaper than the tube and you stay above ground where the sights are, but it's slow going sometimes because of the traffic.

It's hard to say what's a good district to stay, you'll likely be in the western side of the city. Do check the hostels, you can get an entire room for your family much much less than a hotel. There are lots of places around Earl's Court. Kensington is nicer but more expensive.

I know that Rick Steves' books on these two greatest cities in the entire universe has far more information than I can provide.

Heather
As long as you're close to the tube, pretty much any part of London is a great place. Some are higher end, but I've stayed all over, even as far as the Heathrow airport (not recommended.. waaay too far!).

I would only recommend the London Pass if you plan on running around London like a headless chicken. In order to break even you'd have to visit 4 attractions per day, and most places takes 2 or 3 hours. With 6 people, you'll be exhausted.

Most of the attractions don't have a long line.
If you really want to use the pass, I'd buy a one day no transport.

In London you can use the travel pass, or buy an Oyster card (which is a preloaded transport pass). Use the search box to see the difference on these passes, as there's plenty of discussion on this topic.

You won't be able to see everything in London, so just pick some things you really want to. I recommend the London Eye. Yes its touristy, but the view is wonderful, and it makes a great picture for the family.

As for Paris, I used paris-interiors.com but it looks like he only has 2 bedrooms.. not sure if it accommodates 6 people. Use the search box for other apartment companies people have used.

One attraction I really liked was a Catacombs. I did a blog on the trip.. PM me if you want to see it.

Like London, you'll not see all of Paris. That is why we go back to finish what we begin.

I just returned from an almost identical trip with my family - me, my wife and 4 young adult children. Some suggestions: Look into renting a flat in both places. A flat is much more fun than 3 hotel rooms, and you get a better feel for being a temporary local. For London I can highly recommend English Manner - http://english-manner.com - super easy to work with, US based office, all transactions in dollars, nice flats. I stayed in Kinnerton street 3BR and would recommend it - super location two blocks from Knightsbride or Hyde Park corner tubes. I have stayed in four neighborhoods in London, all were good. Key is being close to the tube. Would recommend Belgravia near Victoria, Kensington, or area near the Marble Arch.
If you have a family get the Pass in London. The Oyster card pay as you go is hard to refill by credit card if you have many travelers. I learned this the hard way. The systems on the metro will only let you swipe the same CC twice then they block it out for security purposes. Not convenient if you are trying to reload 6 Oyster cards.
In my opinion the only way to go from London to Paris is the Eurostar. Buy in advance and it is cheap. My whole family traveled for $450, it is quick 2.25 hours out of St. Pancras (get there by tube) and you arrive at Gare Nord instead of CDG. Best part is security and passport control is nothing compared to the airport. Plus the experience is great. You can get the tickets through Rick's web site and even adults under 25 are still considered "youth" rates.
I also rented a flat is Paris, and the experience was good, but far more complex. All contracts were in French, had to pay in wire transfer, had to have 3000 euros security deposit in CASH when I arrived. In the end the flat was fantastic and experience good, but it was much more detailed to pull off than London. I used PariStay - a broker - to make arrangements.
Have a fantastic time.

A suggestion about my favorite topic - FOOD! Every time we go to England we always eat several meals at Marks & Spencer. M&S is a fabulous department store chain that you can find everywhere in London. The larger stores have a supermarket on the lower level of the store along with a wide selection of prepared food such as salads, sandwiches, fruit & vegetables that are portioned and packaged just right for take out. You'll also find M&S Simply Food which (as the name implies) sells prepared food almost exclusively. The food is always extremely fresh (high turnover), a good variety to choose from, and you can really save money compared with going to restaurants. A pasta salad or chicken salad sandwich is such a welcome change from greasy fast food especially when traveling. We have had many, many wonderful M&S picnic lunches in England's lovely parks. On a completely different topic: I always take a top sheet (not fitted) to Europe/UK because most of the beds have only a duvet and no top sheet. I guess I'm too accustomed to my American ways but I find it too hot with it on, too cold with it off. A sheet has made all the difference in being able to sleep well. A warning: The first time I went to Britain I planned to just "check it off my to-do list." I loved it so much that we go there every year now because it is my absolute favorite place to travel. Hope your experience is as good.