We were there last summer and moorings are few - it depends where you're heading for afterwards. As noted by Gianfranco; there are plenty in NW Corsica at Calvi, which are run by the harbourmaster

There were also moorings at Campomoro in SW Corsica, whilst these are I think privately owned, we saw some foriegn flagged vessels on them; I presume you have to negotiate with the owner? Connections from here are likely to be difficult though.

Whilst there are no moorings, the cost of a berth at Castelsardo in NW Sardinia is probably no more expensive than a mooring in Calvi and it never seemed to get too busy. There are regular busses from her to Alghero for Ryanair Flights.

The only other option I could think of is Portoferraio, the main town on the island of Elba (50M east from Corsica), there are sheltered moorings available here and good ferry connections to the Italian mainland.