Hi!
My kids have recently started taking Karate with Sensei Mark and he seems fantastic. His webpage is a bit flukely, but I found this:
https://www.facebook.com/chappaquakarate
I know that he teaches a class for little guys in the early afternoons a couple of days a week - just started that.
Your local parks and rec will probably have classes, I think that some of the preschools have afternoon "enrichment classes".
Perhaps call some of the music schools? There is also this:
Jodi's Gym | Children's Gym | Mt. Kisco, Westchester, NY
Good luck!