October through April is comfortable — mild days, cool nights, occasional cold snaps in January and February. May through September is hot and humid Deep South weather, with afternoon temperatures regularly above 90°F (32°C) and high humidity that makes walking the downtown sights uncomfortable.
If you can plan around a date, the city's most resonant moments fall on the first weekend in March (the Selma-to-Montgomery march commemorations and Bloody Sunday anniversary in nearby Selma), and 4 March (Confederate Memorial Day events at the Capitol, mostly of interest for the contrast). The Alabama Shakespeare Festival runs year-round.