Like most parts of the country, there are many summer "Festivals" scattered around upstate NY. Whether or not you want to attend them depends on how comfortable you are with dealing with crowds, but during them they do fill up local campgrounds.
A couple that I've enjoyed include
Spiediefest, a food & hot air balloon festival in Binghamton, NY (
Some of my photos),
Harborfest, a weekend festival culminating in an excellent fireworks display (
Some of my photos).
I have also enjoyed
Sunday lawn concerts at the Sodus Point Lighthouse.
There is something to do every day just about anywhere in upstate NY during the summers - a Google search for
NY Summer Festivals will highlight what is available on the large scale, stops at local Visitor Centers will help find the smaller ones.