Most budget hotels are ex hostels, so don't expect luxury or even your own bathroom!
There are nicer budget hotels nearer to the museum district, although it's a good 15min walk to the centre. The tram network is brilliant so it won't matter if you're too far out of the main centre. The Dungeon is on Rokin, just off Dam Square.
Here are three hotels I've stayed at.
Trianon Hotel
http://maps.google.co.uk/maps/place?cid ... n=0,0&z=18
Not too shabby, in the museum district, supermarket over the road, good tram links, 20-25min walk to Dam Square/RLD/central station.
Keizersgracht
I can't recall the name of the hotel but it was on Keizersgracht - I think it may have gone - but the location was spot on. 5-10min walk to centre/Square/RLD/train station, 5mins from tram network. It was also relatvely quiet. If you can, stay along this road imo.
Travel Hotel
http://www.hotels.nl/amsterdam/travel/
Very central - the RLD, Dam Square and central station are within 5mins walk. Very noisy at night (the church bells! Arrggghhhh!), but good value for money.
As I've done Amsterdam's main touristy things, if I were to head back, I'd probably stay near the Trianon Hotel (or at the hotel itself) again.
I really love Amsterdam and would happily answer any further questions.