I would definitely cut out Summer, but the other two are more difficult to decide between and come down to personal taste. Yes, Band's Visit is the superior musical and has the accolades to prove it. But it is certainly not a piece for everyone. Its much slower paced and lacks a traditional narrative structure with a clear "ending," but I personally found it refreshingly different and beautiful.
Mean Girls is a big dumb musical with mediocre, but definitely catchy, songs and some decent jokes sprinkled in for good measure. I actually liked the book scenes more than the songs and was looking forward to them ending so I could hear more of Tina Fey's writing. It's fun, especially if you like the movie, but Band's Visit feels special in a way Mean Girls isn't.
Essentially, you're looking at two very different nights of theater. If I were to pick one to see again, it would be Band's Visit.