Hola Edel,
When I stayed in Salamanca in 2001, Garamond was the place to go. It's right near the plaza and easy to find. Things don't get started until about 2:00 am. When you get change from the bar, the pesetas used to have a garamond sticker on them. really good keepsake. Not sure about the euros. If at all possible, met a native salamancan and have them take you to all the neat places. I was lucky enough to meet some guys from barcelona who went to the university. They took me around and experienced the true spanish night life.
Camelot is also good. The Irish Rover is good but mostly foreigners.
La Chupiteria is a MUST! Basically its where everyone goes to get drunk, very cheaply, before the discos. Its a local spot, but you will find yourself frequently returning. Try "La Chupa De La Casa". It's the house special. La Chupiteria is located to the south of the plaza, tucked in a little corner.
Well, now that you are well equipped for your night, don't forget the "churros con chocolate" after. It helps to ease the hang over.
Bien viaje!