Corsica climbing

Hi,
People were helpful here when I asked about climbing near Marseille, and a lot of people mentioned Corsica as a good climbing place for France in that thread, so I thought I'd ask for more specific details here:
Are there any places that would be acceptable to climb in August in Corsica? I'm going there for work (near Cap Corse) for all of July and have a week in August to explore (I know, the most crowded/hot time for Corsica, but it's how it worked out). A climber friend is meeting me and we'd be interested in maybe a bit of climbing (easy trad, sport, deep water soloing) in between hiking/sitting on the beach/siteseeing/etc. Any recommendations?

Also anything that is not to miss in Corsica? Climbing or otherwise? (best beaches, maybe?).

(I'm planning to ask these questions on the French website Camp2Camp, as well).

Thanks!