
Barcelona, Spain is a great summer student destination.
First things first, there are dozens a hostels all throughout the city. Right in the heart of La Rambla (the main street in town that leads to the waterfront) there are a few, but if full, there are many away from the city center and up the mountain. Although further away from the action, there is a metro and good bus service, and lodging on higher ground can also be quite scenic; very beautiful.
For sports fans, an obvious destination is the home field for FC Barcelona soccer club. You can take the metro right from La Rambla and then its a couple blocks walk to get to Nou Camp. If you're unsure you're going the right way all you need to say is "Barca" and the local people will gesture you where to go. The stadium is enormous and the stadium tour is really cool and goes through an extensive museum.
For the arts, there are museums everywhere. Pick up a city map (at a bus or train station among other places) and there will be symbols denoting all the museums. Unless you stay for a couple of weeks it would be impossible to see all of them. Make sure to bring your student card with you for entrance discounts because it can get pricey. I recommend the Gaudi museum. It's located within walking distance of La Rambla if you go north. The house is the museum; the architecture is extremely unique. You will probably use up the SD card in your digital camera wanting to take photos of all the little odd things in the structure!
The nightlife in Barca is exceptional. The city never sleeps and is the international home of electronic music. If that's not to your taste, there's also scenes for jazz, rock, Latin rhythms and pop. If you're staying by La Rambla you're pretty much in the thick of things, but the city has five large distinct areas for its nightlife. For more information, visit the official Barca tourism site for nightlife.