Basically, any time school is in session. Also, note that the southern states end school in May and start mid August. He northern states go from Labor Day till mid June.
September is hurricane season and hence many avoid it - hence lower price. Dec-Feb can be chilly in the Bahamas, but Caribbean is still nice and balmy. Water is choppy though.
Avoid, presidents week, easter week before and after, Halloween, thanksgiving, xmas, New Years.