Kentuck campground in the state park has about 2 dozen walk-in sites, and a bunch of sites that allow dogs. Only a few of the walk-in sites allow dogs, and they're fairly close to sites with electric that are presumably much more likely to have trailers or RVs. There aren't really any sites specifically for tents, but plenty without electric. Based on where things are you may find that a drive up non-electric site is your best bet. You can find the campground map here:
Since you're from Philly you may already know that PA state parks prohibit alcohol. I know that plenty of it gets drunk in the park anyway, but I've also heard of people being thrown out because a ranger saw (unopened) beer in their cooler.
There are several private campgrounds in the area. I don't know much about them, but I expect that some allow dogs.