Brussels is an AMAZING city, both for hanging out, getting drunk, and being riffraff in general, and for being cultured and checking out architecture, museums, awesome food, what have you. It's one of the coolest places I've ever been too, hands down. A trip to Luxembourg is never wasted either, it's not as modern as Brussels and there is less to do, but there's this freakishly beautiful park pretty much in a giant gorge in the middle of the city, like, imagine a beautiful woodland paradise, and around that paradise on all sides is a gorgeous marble European city. It's unreal.
Most my time in Europe was spent going down the Rhine in Western Germany, which is also recommended if you're a Nature sort. The hills on either side are full of castles you can climb up to and be a hoodlum in, the woods are wild and free and to the south in the Ahr Valley they grow grapevines along the sides of the hills and brew EXCELLENT wines from them, and when the mist rises, you fully believe that there are probably mermaids with magical golden rings in the river just like in the operas.
And I don't know if a person can backpack to Venice but if it can be done, make it so. Venice has gotten more touristy but its still worth it.
EDIT: oh holy shit be careful going to Munich during the Fest. It's PACKED, it can get dangerous, you can get robbed, hotels are probably impossible to find unless you book now. I didn't even try, I stayed in Bonn where I was at the time. Oh, also, stop by Koeln and see the Cathedral there, since I'm thinking of Bonn/Koeln. Love that fucking Cathedral. It's RIGHT outside central station, you walk out into the square and see it rising like an armory that gained its own sentience and decided to fuse together and make a giant black iron wrought beast in the road.