Unity Hostel Budapest
This is a very centrally located hostel, and it's two floors. Even though it's a small hostel, it gives off a big feeling. It's clean, has free internet and breakfast, nice and friendly staff, it's closer to the Opera and the main streets in the center of the capital, next to several metro stops and about five minutes' walk from the Danube. The building looks a little decrepit, but it's ok, the hostel is clean and it's in front of the conservatory, so you'll hear music most mornings.
Highly recommendable, the price per bed in each room is between 15 and 18 euros.