In reply to Imogen Gray:
Lots of options. Take a look on the crag map on here and refine by bouldering. But obvious places closest to Sheffield are:
Burbage North
Burbage South
Higgar Tor
Stanage Far Right
Stanage Plantation
Curbar
Froggat
Off the top of my head these are the main spots and there are a good range of grades in most of the spots. Worth getting one of the two main bouldering guides for the Peak.
Further afield there are loads of other good spots in the Peak.
Worth looking at Psychi for a cheaper new mat if you are finding it difficult to get a second hand one. Climbing Works hire out mats whilst you are trying to find a mat.