Geneva, at the north end of Seneca lake, is experiencing a revitalization and has a great wine bar and several very good restaurants. There's a state park with swimming beach access and a splash pad just east of town.
In addition to Taughannock and Buttermilk, I'd highly recommend the park at Watkins Glen. Many of the parks have camping, but may be largely booked for the summer months by this point. Still, worth exploring.
For kid stuff, in addition to parks, there's a natural history museum just outside Ithaca (Museum of the Earth). If you make it up to Rochester, there's a fantastic children's museum (Strong Museum of Play). But kids would have plenty of fund in the various parks in the area without needing anything else.
Most FLX wine is not good, but there are some exceptions, if you want to stop off somewhere. Ravines and Dr Konstantin Frank are two of the most prominent.