Based on statistics from the U.S. Bureau of Transportation Statistics this interactive map developed by analytics site Five Thirty Eight not only tells you the airports to use but the most reliable airlines as well. Five Thirty Eight was developed by Nate Silver, author of the excellent book I read a few years ago, The Signal And The Noise, giving me confidence this analysis is very thorough. The map is updated in real time.
The Signal and the Noise: Why So Many Predictions Fail–but Some Don’t