Bastia was the city I visited in Corsica. Took a direct flight from Barcelona. Takes only an hour to reach here. You can rent a car to downtown Bastia or you can board the official bus that is available every hour from the airport.
(Make sure you book your hotel in advance as availability of hotel rooms in ON season is too less, I had to change my hotel every day)
Stayed at Hotel Posta Vecchia. Small and cozy, near the dock of Corsica Ferries, downtown market and the famous lighthouse. Location of this hotel was the best
Visited the museum where matargashti song from film tamasha was shot , the lighthouse and walked through the mustard themed streets of bastia .
Tip : Collect maps of this city from the Tourism Office when you visit it. Like a kid drawing from school, easy to read and very resourceful .