London and Paris (maybe Amsterdam/Brussels too?) in 10 days

With such enormous, major cities, I don't think adding any more would be a good idea. For both of them, there are some great side trips you could do by public transportation if the spirit moves you. Have a wonderful time!

I'm still voting for just two cities for you guys. But if you add a 3rd, I wouldn't vote for Brussels. It's distinctly less...I don't know...something than Paris and London. There's some good sites there, but I would leave it off this trip.

If you haven't been to Europe in 20 years and it's your daughter's first trip, I would stick to the simple two city route. Amsterdam is a nice city too...if you decide to add it in, I wouldn't suggest driving from there to Paris. Renting a car and driving it one way down to Paris will be very expensive and a long day's drive for you. Plus, I'm not sure what kind of winter driving conditions you might still find in March. Train would be simpler. If you add Amsterdam, you wouldn't likely have time for "other cities" - a good split would be London - 3 nights, Amsterdam - 3 nights and Paris 4 nights.

London.. with daytrip to Bath.. then Eurostar to Paris.. with daytrip to Versailles or Chartres .
If I was to add one more place ( which honestly I likely wouldn't) I would change it to London, to Amsterdam to Paris.. giving London and Paris bulk of time..

First, no, you don't have 10 days. You leave on March 19. Your flight arrives in Europe sometime on March 20 - no? So you really only have 9 full days (March 21-29) in Europe. Don't count your arrival or departure days - those days are consumed by other things. At best, on your arrival day you get to walk around a bit (trying to stay awake, waiting for your hotel to let you check in, etc.). And the next day, you'll probably be at least somewhat jet-lagged, so most people are not 100% on that day. On top of that, the day you move from London to Paris will be largely lost to the (admittedly short) trip along with getting oriented in Paris, finding your hotel, etc. Your departure day is consumed by packing, checking out, getting to the airport, security, freaking out because you misplaced something, etc.

So start by being honest with your self about how much time you really have. You have 8 full usable days in Europe, not 10.

That said, I'd suggest you not try to add a third destination. With just 4 days in London and 4 days in Paris, that's a nice little taste of Europe.

I'd stick with London and Paris. You could stay for years in both cities and still find more to explore.

I took a 10-day trip from London-Paris with my dad when I was 16, 10 years ago (5 days in London and 4 days in Paris) and we didn't feel like we had enough time in Paris, so I definitely would not add another city to your itinerary. I'm also taking a London-Paris trip with my husband in May (3 days in London, and 7 days in Paris, excluding the 2 flight days to London and from Paris back home).
What my dad and I learned from our trip to London and Paris:
Don't
Don't go to Bath {it's not as beautiful or impressive as anything in London, and it's overcrowded (i.e. it feels like a tourist trap)}
Don't go to Stonehenge (it's no more interesting than looking at a photo, and I had a tour guide)
Don't take a tour-bus ride out of either city; it feels like a tourist trap and wasn't memorable

Don't go to the Eiffel Tower if it's crowded (the crowds in the Tower and in the elevator through the Tower are massive and so is the opportunity to be pick-pocketed).
Do
Do take a tour of the Tower of London (the tour guides are very passionate and funny)
Do visit Saint Paul's Cathedral
Do visit Westminster Abbey
Do visit Shakespeare's Globe Theatre and see a show there (I didn't get to see a show in the theatre with my dad, but I'm planning on buying tickets before my trip this year)
Do have tea in London
Do take a river cruise on the Seine
Do see the Eiffel Tower at night
Do go to the Louvre, but at an unpopular hour and day so it's not too crowded to see the art
Do visit Notre Dame (I wish we had stayed for a service there, but my dad and I hadn't planned it and didn't have time)
Do visit Sainte Chapelle (extraordinarily beautiful)
Do go to cafes
Do reserve a table in the Eiffel Tower Restaurant before your trip if you want to be in the Tower and avoid crowds (there is a private elevator for restaurant patrons)
*note: I didn't see Versailles with my dad, but I wish I had

Er i loved Bath, the Baths alone are worth a visit just to see the ancient Roman ruins. My daugnter loved visiting the Clothing Museum, dresses and fashions from medival times thru 20 century. ..
And for those who have read and loved Jane Austens books( or seen the movies ) Bath has its own charms.

I think the thing is , your daughter needs to do some research and come up with some ideaeas of what would interest her, i had my kids do that, at 11 and 13, so a 16 yr old is more then capable of investing a little research equity into a wonderful trip that you are paying for!

I do agree that Stonehenge was not our thing, but some folķs love seeing them.

I also would not feel the need to add a third city to the list, but if you do add Amsterdam, then fly there from London on EasyJet for about $45 per person (note that different departures use different London airports). Either the London-Paris Eurostar ticket or the Amsterdam-Paris Thalys train ticket can be expensive at the last minute and cheaper if you reserve them now.

To add to the chorus: I think with 10 days, you'd be better off sticking to London and Paris. I've not been to Paris, but having spent 5 days in London before, I still feel like I have a ton to see.

I will say though, I have to disagree about the Tower of London. We chose to go there partially based on praise from Rick's book, and IMO it was by far the cheesiest tourist trap I experienced in London, and not worth the 20 quid. At least we ended up getting free tickets to see a play at the Globe, so at least I feel like that cancelled out the wasted money spent on the Tower.

Thanks, everyone, for the great tips! I decided to stick with just London and Paris because of your advice! Now, for the booking of all of the museums and other touristy places to go.