Lisbon is full of places to stay. The central International Youth Hostel is nice, although noisy because of the way it is built. You may be able to reserve a private room if you act quick. It's better to stay on the OUTSIDE of the building if you have a choice as it's built like a big "O" with stairs up the middle so even if you're on the top floor, noisy party people coming in a 2 am will wake you up b/c the noise travels up the center. But it's nice, clean, and VERY convenient.
The Youth Hostel out at the coast is nicer, in my opinion, and quieter, but a bit of a walk into town. We also found an nice ensuite room up close to the Castelo with a great view for 34 euro.
There are little pensiones everywhere, usually advertised above your head as you walk... just go in and ask to see the room.
You might consider taking the train (very short trip) to Sintra and staying at the hostel there.. last time I stayed it was only 9 euro, could be more now. LOVELY, and plenty to see there, and a short train ride into Lisbon.
Eat bacalau while you're in Lisbon and don't miss the Museu de Coches (Museum of the Coaches) and the Military Musem. Both are really fascinating!