Spring (March–May) and fall (September–November) are the best times to visit. Temperatures are mild — highs in the 70s°F — and the humidity is bearable. Spring is also when the azaleas bloom across the city, which is genuinely worth seeing.
Summer is hot and humid, with afternoon thunderstorms almost every day. Highs regularly reach the mid-90s°F with heavy humidity. The university empties out, which quiets the city considerably.
Winter is mild by most standards — rarely below freezing — but can be grey and rainy. The legislative session runs in spring and early fall, filling the city with lawmakers and lobbyists, which affects restaurant reservations more than anything else.
FSU home football games in fall (September–November) bring the city to life in a way that's hard to overstate. If you are even mildly interested in college football, attending a game at Doak Campbell Stadium is an experience.