I backpacked france, spain, italy, and the netherlands for 5 weeks after high school....was the most amazing trip ever. A lot of the stuff has been pointed out already so I'll keep it short.
Spain
Madrid- I intended to stay in madrid for 4 days but ended up leaving after 2 because it's not that great of a city. Pretty trashy and has lots of pick pockets: keep everything important on an inside pocket or something, they are very skilled and don't hesitate at the fact that other people are watching them (also, they're probably armed so don't be a hero -learned this the hard way.)
Barcelona- AWESOME, So much cool stuff in barcelona, the beaches, the sagrada familia, the parks, the boardwalks, bars, etc.
Seville- also cool, but not worth more than a day or two.
France
Paris- So much to do, give yourself a few days here, you will regret it if you don't. Food-don't eat on champs elysees or any other famous avenue, you will get ripped off on really shitty food. Go find a little hole in the wall restaraurant, it will 10 times cheaper and infinitely better.
Alps- beautiful mountains with lots of great activities in the summer. Go to a ski town like tignes or avoriaz and do some hiking, biking, hang gliding, rock climbing, etc. Also, both tignes and les 2 alpes have glaciers if you want to ski.
Nice- awesome city, best of both beaches and mountains. Visit Eze, its a small village about 3 miles out of nice and is really historic with lots of great artisans. Also, make a trip to monaco and ask a local for a good beach to visit. Oh and stay at this place Villa Saint Exupery: it's an old monastery thats been converted into a hostel- awesome staff (smoked hash in the bar with the staff), awesome food, cheap booze.
Loire valley- lots of castles, history, and fastatic food and wine. Tours, blois, and orleans are all good places to stay. Go for a bicycle tour of the castles.
Italy
Venice- Wasn't a big fan, the water smelled pretty bad and it's just one big tourist trap. The city is only alive because of tourism so it's only tourists, vendors, and pigeons. Everything is overpriced- don't stay in venice itself, find a place on the mainland.
Florence and the surrounding areas- Probably second favorite city next to Nice, lots of history and famous art is kept here. Don't leave the historical area at night- I got chased by muggers across a bridge. Really beautiful countryside, go on a bicycle winetasting tour- riding a bike while hammered on great wine= awesome. Go for a hike, visit villages, etc.
Rome- So much stuff to do it's overwhelming. Already accept the fact that you won't get to visit everything and you will have a better time. Free drinking fountains are actually clean and really great because it gets HOT.  Ride the subway, its an experience and watch out for crazed gypsies.