I recall driving through Horseheads, and it has a very charming old-fashioned-looking downtown.

I would second the suggestion about Ithaca -- I stayed there for a summer and it was great fun. Maybe the kids would enjoy the children's science museum there?

One other option for lodging is the Hotel at Cornell, which is staffed by students at Cornell's hospitality program, reputed to be one of the best in the country.
http://www.statlerhotel.cornell.edu
Although this may be a bit pricey and maybe wouldn't be quite right for the kids.