there's one called the Peace Hotel i think, it's a B&B, on the corner of Endcliffe Park - road is Brocco Bank. Obviously never have had to use it so can't recommend it or not, but it looks nice and is a 5 min bus ride from he centre.
There are a few around here which is very central (30 mins walk and 10 mins bus to the centre).
There's one on Wostenholm Road. My friends family stayed there when they came to her degree show a few years ago and they said it was OK if you just want something simple.
I stayed at 2 on that road when I first came here.
I was in Lindum Hotel for a month and Nether Edge Hotel for a fortnight , both nice enough and on a bus route to town.
You're looking at about 35 - 45 quid a night.