oh, just outside NY City are the Gunks... http://en.wikipedia.org/wiki/Shawangunk_Ridge which are worth a stop... We always camped in someone's field with all the other climbers, a creek for a shower, but there should be lots in the area that would fit the bill. The cliffs are stunning and there's a lovely crushed limestone path along the base, not sure about bikes/pets policies but I don't remember it being particularly restrictive other than climbing activities.
Minnewaska Preserve touches Mowhonk Preserve but is a State preserve, http://nysparks.state.ny.us/parks/127/amenities-activities.aspx and DOES allow biking for sure, but I'm not sure where to camp nearby (there have to be places, it's a really popular and beautiful place).
Both are ~7-9 hours away from Pgh, depending on how you drive, so may not be as far as you'd like if you're sleeping 1 night in PA.
Have fun, and share what you find?