What sort of shooting do you want to do? There's Dowry Hill in Groby although I'm unsure of opening times. Kibworth which is open all day Tuesday to Sunday and has 3 air gun ranges and a very fine HFT course setup once a fortnight (even if I do say so myself!). I'm sure there are others in the West Mids but it's not my neck of the woods and I'm very happy at Kibworth.
If you want to pay us a visit, drop me a pm and we'll arrange something!.
Ryan