Somewhere between Ithaca NY and Geneva NY is this ice cream store that sells wine ice cream. As I am not of age, I didn't try any. However, they also have lots of other ice cream. I bought a "small" mint chip ice cream whose scoop ended up being larger than my fist. It was also only $2.60. I'm not sure whether they make all these normal ice cream flavors on-site though, because I saw a Hershey Ice Cream sign, and the mint ice cream tasted pretty normal.
The lady at the resgister seemed a bit irked and impatient but that might've been because there were 13 of us causing a ruckus and/or paying with card (which required signature).
I am unable to recall the name of the place and I can't find it on Yelp or Google Maps. It was somewhere between Geneva and Ithaca and I think it was a sky-blue cottage off the "highway".