Wagner Vineyards on Seneca Lake has a nice warm weather outdoor cafe with great views of vineyards and the lake - lite fare- soup and sandwiches and their own wine and beer. Goodplace for kids.
Glenora, also on Seneca, has an excellent upscale restaurant and a very comfortable Inn.
Castel Grisch also has a nice patio for dining at reasonable prices.
If the kids are young, its OK to take them to Bully Hill for hot dogs and hamburgers. The tasting room is run like a big frat party with the quality of wine to match.
PennYan has a number of small more roadfood type places that have good hamburgers, etc.
We've never found any speedies or any take out Cornell chicken around the lakes, but it must be there...
Dont fail to go to Herman Wiemer's winery on Seneca - at least as good as Franks - and we love Franks!
BTW: As we passed through Ohio last Fall we bought a half dozen bottles of Ohio wine - all of it inexpensive and none of it worth the trip.
I'm sure there's good stuff there- we just didn't find it.