Transportation - train. High speed TGV from Barca to Avignon - base your time in Provence around the

First let me say that this is the first time I have used this site. You guys are awesome! What seems like such a daunting task now feels at least a bit doable. So here is my question. My wife, 2- 20+ year old daughters and I want to start our trip In Barcelona on June 26th , head to Provence, Paris and ultimately end up in London on July 5th. We are open to your suggestions for mode of transportation, ideas for areas within the cities mentioned, length of time in each city and otherwise eager to get your feedback. Budget is as always a consideration but not an overriding factor. Meaning, no hostels but don't need 5 star either. Thank you in advance for your time, I look forward to the day when i can be of assistance to others!
As for transport - in Barcelona and Paris public transport is the way to go. But in Provence it is best to have a car. But w/ just 9 days you'd really do better to limit yourselves to Barcelona and Paris. (I assume land and cruise alaska packages that any time in London is not included in your '10 days')
Transportation - train. High speed TGV from Barca to Avignon - base your time in Provence land and cruise alaska packages around there. then TGV to Paris and then Eurostar to London. In Provence the Roman amphitheatre in Orange, Pont-du-Gard land and cruise alaska packages and the walled city and Palais du Papes in Avignon are all worth it. And do some wine tasting at Chateau Neuf du Pape. You could rent a car at the train stn in Avignon land and cruise alaska packages - most are there - I've used Avis. There's land and cruise alaska packages plenty land and cruise alaska packages of info on what to do in London, Paris and Barca in tour guides etc... but if you have more specific questions just ask
Personally I'd keep it simple. You have 10 days to start in Barcelona and end in London (where I assume you'll have at least 4 days). Assuming you are coming into Barcelona land and cruise alaska packages after a transatlantic or long flight your first day will likely be jetlagged. I'd divide my time between Barcelona and Paris. 5 days in each city will give you enough time for perhaps a daytrip or maybe 2. But you'll find plenty to occupy you in Barcelona and Paris. I'd fly between Barcelona and Paris as you can find inexpensive fares and it's a time saver.
You may consider renting apartments. With 4 adults you're going to need 2 hotel rooms. An apartment will likely be less expensive than 2 hotel rooms and you'll have more space. Of course, given this is your first trip to Europe you may not feel comfortable renting an apartment. If so, then it may help to get a feel for the amount you are willing to spend per night for lodging for all of you.
Due to a recent upgrade, if you have been using a social sign on prior to 2/28/13, you will need to create a Fodor's password and link your new and old accounts. If you don't have a Fodor's password, please request one by emailing us at registration@fodors.com . We apologize for any inconvenience.