Don't immerse yourself in one place, there's SO MUCH to see in Europe. Get a Rick Steves book and follow his advice...he also has shows on PBS that are great.
Do your homework and planning BEFORE you go.
oops...forgot about London.....I lived there for a year, but you can see a ton in 2 days.
Speaking of London, if you go there, do the “London Walks” tours. The best thing about them is you can just show up, and they are fairly inexpensive. I believe they also have similar tours for Paris, as well.