Mike,
Allegany State Park is in NY and
Allegheny National Forest is right across the border in PA.
It's been 20 years for me, but the Red House area was pretty nice then. They might have a pool now, but back then they had a beach and cabins. The beach was always crowded on weekends and the cabins were rustic, had electricity, but always filled up fast on weekends. There are some very easy walking trails with short 30 minute - 2 hour hikes , but it has been too long to remember the details.
If you venture into PA, the Kinzua Dam and a drive along the Allegheny Reservoir is nice. There are some hiking options on the Morrison Rimrock Trail, but these are longer loops of around 8 and 5 miles (think of a north loop and a south loop that connect in the middle).
The North Country Trail winds through the Allegheny National Forest. In NY State, it becomes the Finger Lakes Trail and heads East across the Southern Tier and through Letchworth State Park (indeed a spectacular place, which I visited regularly over until we moved away 7 year ago.) you can camp at Letchworth in several campgrounds.
Once at Letchworth you are a short drive away from some of the Finger Lakes as well.
OK, So where the Finger Lakes Trail turns East, by Salamanca NY, Another Trail shoots North - This is called the Conservation Trail - Maintained by the Foothills Trail Club of Western NY. This trail takes you past old CCC camps and along the top of Holiday Valley/Holimont Ski slopes. but in addition, it takes you by
Little Rock City (
map)- A great place to take the kids (
similar to Thunder Rocks in Allegany State Park, if you go). This is an area where soil creep has caused a huge wall/table of rocks (~1/2 mile long and ~1/4 mile wide) to start to break apart in car and building size blocks and slowly creep down the hill creating little streets and avenues between them, there are several small picnic pavilions and there use to be restrooms. very scenic and remote, at the end of a long dirt road on top of a forested hill, (if you decide to drive). There is also "Rock City in the Southern Tier near Olean and Panama Rocks over by Jamestown. they are a little larger than Little Rock City, but I have only been to those places once and frankly cannot remember the details of each.
You will find there is a lot to do and see in western NY and the Southern Tier. Much more than I can talk about in 15 minutes. I'd be glad to answer any questions, a the are was my stomping ground for many years, but my info is at least 7-20 years old depending on the area..