Jazz,
Great, that sounds kinda like what we want. The trip I linked to isn't a tour thing at all, just a package of flight + hotel, and it changes from London to Paris to Rome after every 3 days, with a train ride between them (also part of the package).
All sightseeing, tours, meals is up to us, which I think will be half the fun anyway. I am a little concerned about not being able to communicate well in Rome and Paris, but I hope they will have mercy on a dumb american.