I stayed at Unity Hostel for 4 nights last month and had a great time!
The staff was friendly and very helpful, handing me a map and providing directions to some of the sights I wanted to see. They even helped me book a caving excursion which was amazing (and cheap) and got a bunch of us pumped to go to a local spa party at Szcehnyi.
The hostel is located in a perfect location, close to the Octagon and public transit. You can easily walk towards Heroes Square in 15-20 mins and to the Danube in about the same time. It's also close to the ruin pubs which Budapest has become so famous for.
The hostel is located in a residential building which makes you feel very at home. Although you need to be quiet at night to respect other tenants in the building, there is no curfew enforced.
I like that the hostel has a limited number of rooms. I found myself quite liking all the different people there and can easily say, it was the best time I've ever had at a hostel. Our entire room of 8 actually all went out together on more than one night!
Although the breakfast is "all you can eat", it would be nice to have some fruit options added like apples or oranges, instead of just cereal and toast. Only other improvement needed is a much faster Internet connection.
Should I return to Budapest (and I will be soon), I'll be staying once more at Unity Hostel.