Yow know Girona is quite far away? I just checked online and it's over 80km. Good old Ryan Air! So if you've an early flight you might want to reconsider staying in Barca the night before.
We stayed in Hotel Sant Agustin off La Rambla. It was 50 euro a night per person, 3 star. Very mediocre but the location was class. Well, it was McDodgey, but close to everything. Try and aim to be around La Rambla or Placa de Catalunya. The old Gothic area (the opposite side of La Rambla to that hotel) is the nicest to mooch around at night to find bars. Barcelonetta is by the sea, bit touristy but still nice.
There are a million hostels if you're looking for something cheaper. The one next to our hotel was called Hostal Ramos, I think. But you'll probably just have to trawl the 'net.
Don't let your girlfriend bring a handbag out at night. There's serious crime there, especially around La Rambla, and pickpockets all over the place. We wore jeans, took a small bit of cash, no credit cards, bought a disposable camera, and that was it. We had no hassle at all but we were very careful.
Ok, lecture over. Enjoy!