In reply to Yorvik:
We found our two apartments for a fortnight trip via www.Homeaway.com.
We stayed in Corte for a week so that we could climb mainly in Val di Restonica, which is wonderful, but personally I preferred our week staying in Zonza and climbing around Col de Bavella.
You don't say what type of climbing you prefer, but there's sport, as well as real climbing (by which you will infer my preference!) wherever you go.
However difficult it may seem to get it sorted do persevere - Corsica is not to be missed.
Good luck and "bon escalade"