Chichester's summer is busy and rewarding. The Festival Theatre runs April to October, the Festival of Speed in early July fills hotels for fifty miles around, and Glorious Goodwood follows at the end of July. May and June are perhaps the best months — long days, full gardens, no festival crowds.
Autumn is quieter; the Goodwood Revival in September is the last big event of the year. Winter is genuinely off-season and you will have the cathedral, the gardens, and the harbour to yourself. The weather is mild by national standards.