Barcelona is a very tourist place, you can visit a lot of museums, go to great restaurants, and still have fun during the night.
If you are going, you need to hear some advices:
- Be careful in "Las Ramblas": a lot of thieves are looking for naive tourists (i.e. steal wallets, play the "find the ball and bet money", ask you for information and steal your bag, etc... )
- Avoid eating on Las Ramblas, it is very expensive and the food is not great. Go to Paseo de Gracia, Rambla Catalunya, Av. Laietana... all these avenues are near the center.
- If you still don't have a place to stay, I know a hostel named Gothic Point. I went there last summer and I had a great time. The place is big, neat the center, and very close to a subway station. It was not expensive and the breakfast was included.
- To go out in the night, avoid going to Maremagnum.. Ask to a taxi driver to take you to Santalo Street, it is full of bars and near from several discoteques.

I hope this information will be useful for you.