In the village are Union Block (Italian) and Village Tavern (seafood). Just outside the village is Bully Hill Vineyards and its restaurant (I don't care for their wines but the restaurant is very good). Between Hammondsport and Bath is San Carlos Restaurant (Mexican family from Sonora which specializes in beef), and Pleasant Valley Inn (fine dining). Up the lake on Rt54 near the bluff is the Switz (casual with a great view of the lake and bluff to the west). Up the lake on the west side near the bluff is The Waterfront (seafood or steaks). They have lots of outdoor seating right on the lake with a superb view of the bluff looking east. Those would be my recommendations and all are good. For a small village, Hammondsport has several excellent dining spots. If you will be in the area 3rd week of July you can catch the Wine Country Classic Boats show in Hammondsport. In summer the Finger Lakes are as close to heaven as you can get.
Two tourist pointers. If you go to Bully Hill, drive north about 1/2 mile to a lookout on private land. The owners don't mind at all and the view is spectacular. Also take in the view down the west branch of Keuka Lake from the outdoor seating at Esperanza Mansion, just outside Branchport. Good dining there too.