If you want to find cheap flights to Alabama, you might decide to visit between December and February. This is the low season, and everything from the flights to the hotels in Alabama will be cheaper. You won't miss out on great events either, since the Galaxy of Lights, a holiday light show named as one of the Top 15 events in the Southeast, goes on until the end of December.
If you're not worried about the seasonal difference in plane tickets to Alabama, you could fly in during March when spring weather hits the area. During this time, you can see the Battle of Horseshoe Bend Anniversary event in Dadeville; if you snagged a rental car while booking your airfare, you can drive down to Birmingham - which Zagat listed No. 1 on America's Next Hot Food Cities. If this is in your itinerary, it's best to book hotels in Birmingham, Alabama so you don't have to drive far stuffed full of fine Southern cooking.
Regardless of when you visit, you should check out great sites like the USS Alabama, the McWane Science Center, and the U.S. Space & Rocket Center. Book with Travelocity when looking for an airline to visit the great state, since you can save $537 when booking hotels and flights to Alabama simultaneously.