In reply to TradRat:
Lots of good advice on previous posts if you search. Generally, West of the City Centre, especially SW is popular with climbers for the obvious reason it's quick out to the Peak. Further North also decent, Hillsborough (more affordable than Walkley) etc, and Stocksbridge/Deepcar (good links to M1 and northern grit crags too).
I'd seriously consider Chesterfield and Dronfield if proximity to a climbing wall isn't a deal breaker.
Bare in mind the new Sheffield clean air zone if you drive a van. This also covers the ring road (!) and costs £10 a day. Expect this to include all private vehicles at some point, at least one councillor is pushing for it.