Bastia is a year-round city in a way that the beach resorts further south are not: it has a resident population of 40,000 and a working port, so it functions outside the summer season. That said, the climate makes the shoulder seasons — May to June and September to October — the most pleasant for exploring. Temperatures are warm without being oppressive, the tourist crowds are minimal, and the locals are in a better mood.
July and August are hot and busy: the ferry port operates at full capacity, accommodation is expensive and needs booking well in advance, and the city's beaches fill up. The Good Friday Scala Santa procession in spring and the Assumption Day procession on 15 August are both worth planning a visit around if religious spectacle interests you. The Christmas and New Year period is quiet and atmospheric, with the Genoese old town largely free of tourists.
Winter on Corsica is mild but wet. Bastia sees occasional northerly winds off the Ligurian Sea that can be sharp, but snow in the city is virtually unknown.