I think you might enjoy the Choate experience the most … largely cause it has a long standing history of cultivating the Arts. I can’t think of a school with better arts related facilities (Paul Mellon Arts Center, Colony Hall) than Choate.
Among the three, Exeter is the best when it comes to STEM although Exeter’s Goel Center for Theater and Dance is very, very impressive.
Andover is excellent in just about everything and I understand they are contemplating building a new Arts Center.