Might want to start with PA: http://tinyurl.com/2kba4j Some rooting around should produce similar results in neighboring states.

Prince Gallitzin State Park is one of my favorites for this kind of travel: http://www.dcnr.state.pa.us/stateparks/Parks/princegallitzin.aspx

It should definitely be within your driving range and it's a lovely place; the town of Flinton has a few restaurants and stores and is right outside the park. It might be crowded in mid-summer, but you should be okay in late summer/early fall.

I've had some great times here!

Check out the lake erie islands. Very nice in the summer, really relaxing but with lots to do, and close to cedar point amusement park, "roller coast capital of the world".

http://lake-erie.com/

http://www.cedarpoint.com/

www.kelleysisland.com & www.hockinghills.com, there are a few posts on here about each. The Old Mans Cave camping area abuts a Lake. Also, Lake Hope & Lake Logan are both nearby for fishing as well.

Lots of state parks have full-service cabins that fit your description, although I doubt most would allow your dog. Herrington Manor in Maryland and Cacapon State Park in West Virginia are two I can think of off-hand. State park cabins are usually such a great bargain that they fill up quickly, so you may have to act fast to get a cabin for this summer. Deep Creek Lake in Maryland is another suggestion.

I knew this was the right place to ask - such great ideas. Thanks everyone! I am definitely open to further ideas, so keep them coming.

Gee, when I was growing up, the population around Canadohta Lake always quadrupled with people coming in from Pittsburgh!

Perhaps something at Cheat Lake, just northeast of Morgantown, WV., would appeal to you. It's an easy drive from Pittsburgh; the surroundings are lovely!