Although it isn't a place for serious off-roading, some of the roads at Happy Valley can be a bit rough, especially in the early spring or late fall. Although 4 wheel drive isn't a necessity there, it is still a nice place to go and drive down some of the roads, check out the dam and the lake and maybe have a small picnic.
It is perfect for people who just want a place to go that isn't full of crowds, like malls and shopping centers. Happy Valley is located on route 104 outside Mexico, NY, which is north of Syracuse, NY and south of Watertown, NY, off of route 81. According to the DEC website, the exit is exit 34, off route 81.
The place is actually described as a protected state lands area, and there is a DEC office on the property. The property is about 9000 acres total, with roads, some old abandoned farm buildings, the lake, and a few campsites. They do allow overnight camping, but you have to reserve ahead of time. They don't allow alcohol on the site except by permit as far as I know.
ATV's and UTV's are allowed in the summer, and snowmobiles are allowed in the winter once the snow gets deep enough. Also, for you adventurous fisherman, just north of Happy Valley, in Pulaski, NY, is the Salmon
River that has salmon fishing in the late fall and steelhead from October to early spring. The NYS DEC website will have more information on when the season starts and ends for each type of fish.
I know, I sound like a tour guide for Oswego County, but I lived there for quite a few years and loved it there because there were so many things to do summer and winter. Along with touring Happy Valley and fishing, it isn't very far from Lake Ontario, and a couple hours south of the Thousand Islands. There is also dog sled racing, hundreds of miles of snowmobile trails in the winter and ATV racing and trail riding in the summer, boating on Lake Ontario, and a bunch of historical areas for the history buffs—like Fort Ontario in Oswego, which has a very diverse history, or the lighthouses that are scattered up and down Lake Ontario.
Oswego, NY also has a major boating festival in the mid summer, called Harbor Fest, that lasts for an entire week, but you don't have to own a boat to be a part of it. Harbor Fest isn't really an activity for kids, it's mostly to promote the boating and local alcohol-making establishments in the area.