In reply to ClaireMc:
If you decide to add Col de Bavella to your itinerary (and I would) have a look at this:
http://www.auberge-bavella.com/gite-etape-gr20/
Restaurant with dorm type rooms. We stayed in a rented apartment down the road but, charming tho it was, we were quite envious of our friends who stayed at the gite as it's right there on the col - walk out of breakfast straight on to the crags - well, some of 'em, and even onto the famed GR20 if you fancy walking a section of that. Preferred it to Restonica (Corte), though we did great climbs at both areas.
I've no suggestions for Corte as again we stayed in a small private rental which wouldn't do for a larger party. Never climbed around Ajaccio although would like to sample Monte Gozzi.