In reply to Pepper:
There is a very small climbing wall in the sports centre. It doesn't look that inspiring.
Bear rock is all right but I prefer Redpoint in Birmingham, it is a bit further away but it is all motorway so takes about as long (depending on where you are in Rugby).
If you are looking for a bouldering centre try The Climbing Station in Loughborough.
Outside your best bet is Leicester area see:
www.leicestershireclimbs.co.uk/ or www.leicesterclimbs.f9.co.uk/
Post edited at 16:24