Where in Fishkill can I take the kids for gymnastics lessons?

It depends on what you're looking for. If you just want your kids to jump around and have fun I'd take them to Jumpin Jakes, but that's more of a bouncy castle type place. For real gymnastics instruction you should try Gymnastic World. I've never actually done gymnastics, so I can't say for certain that it's a good place for lessons, but it's in Fishkill and will give you options.