We loved Our Place Hostel – it's got a great location (right by Keleti palyaudvar – east station). It's about a five-minute walk from the train station to the hostel. It is also very cheap to stay here.
The staff are very nice. We arrived very early, unexpected (about 6 a.m.) and the guy was still very nice and helpful (we woke him up). He gave us maps and recommended places to see. The people at the hostel are great. We got to meet a lot of English boys there. What seemed odd was that everybody in our room spoke English as their primary language! We never had that happen before.
They have a couch, TV, and a computer in the living room. There are three showers. The hostel has free lockers, you just have to provide your own lock. They also have a kitchen-like room where there is a big refrigerator. We didn't see a stove or cooking utensils.
There is a relatively close bath house nearby, Szochenzyi Baths, about a fifteen- to twenty-minute walk away, depending on how fast you walk. It's really big with many different baths and spa treatments.
We arrived in Budapest during their national holiday. There were fireworks and air races, which were awesome. Budapest is a beautiful city, and staying at this hostel is definitely worth it!
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We did not like this hostel. It was dirty, the toilet didn't work and the host tried to blame us for that. The shower didn't work. The Internet connection didn't work! The host didn't care. Hardly any hot water. We lived with dust bunnies, a dark room, cold nights, and constant sirens from police cars and fire trucks. The only plus was that it was close to the train station, so that we could get away quickly. 
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