I live in the area and drove by it for 30 years on the way to work - I have ate at the Restaurant on occasion.
Easy to get to - looks like the sites should be decent sized.
You may want to try Sunset RV Park and Cabins - - http://sunsetrvpark.net/index.html
Battle Island is a state run golf course south of Oswego on Route 48. Oswego Country club - within city limits on Route 48 (route 48 is on the west side of the river and route 481 is on the other side). Griffins Greens is about 15 miles west of the city - Route 104A.
Forgot to mention that there is a golf course about 1/2 mile from the campground you are thinking of staying at. Tamarac - started about 10 years ago by an RP tech at the power plant.
X2 on the local racing. Watkins Glen race track is about 100 miles from Oswego.