From Bastia Airport, a bus runs almost every hour for €8 - timetable at the tourist information desk at the airport.
There are several national and international ferry routes from Bastia, to Ajaccio (Corsica), Genoa (Italy), Marseille, Nice, Livorno (Italy) and Savona. It is very busy during the summer, and it is always best to book early.
The Vieux Port ('Old Port') is a wonderful part of the city. Tall, faded buildings surround a marina with posh yachts. There's certainly something of the 'shabby chic' about the place.
One great location to eat is in one of the many restaurants in the Vieux Port. Most specialise in seafood.
A daily bus runs to Calvi (€20) as well as all other major Corsican cities, and trains run daily to Corte and Ajaccio.