As Antigua is in the Caribbean, the best weather (least humidity, intense heat and mosquitoes) takes place from about December to May.  However as this is also the most expensive season on the island, going a little before or after that (November-June) could make for a cheaper and far less crowded trip.  Hotels could be up to 40% off during the off season.  Keep in mind, however, that many of the smaller hotels and attractions close between August and October. 

Antigua boasts two well-attended boating festivals.  Sailing Week takes place either in late April or early May, in which a world-class regatta brings an international crowd to the island and several weeks before that, the Antigua Classic Yacht Regatta brings a similar crowd for the 5-day event. 

Carnival takes place in the summer (check a calendar or with local hotels for this year’s date) and lasts for 10 days in an island-wide celebration filled with music, costumes, floats and general revelry.    

October brings another large celebration of music in the form of the Antiguan Jazz Festival which particularly celebrates Afro and Caribbean styles and fusion.  For those who love tennis, Antigua hosts a Tennis Week in the second week of May, with a pro-am tournament and exhibition games.  

For more information on weather and festivals, please refer to the following links:
http://www.sailingweek.com
http://http://www.antiguacarnival.com
http://www.antigua-barbuda.org/Agcal0...
http://www.thetennischannel.com/trave...
http://antigua.caribbeanway.com/weath...