Taughannock Falls SP is a nice park but it has "small" RV sites. We have a 34' 5th wheel and there is only one site that we fit. The rest have a 30' max ... our previous 28' 5th wheel was tight in the 30' sites and I believe they are o top of each other. I think the tent sites are spread out though so a pop up (or similar) might work well in those sites? I have no idea about levelness, I just deal with what we get. You need to drive to get to the swimming area and the waterfall hike. The waterfall hike is quite easy. It seems like they've tried to make the trail wheelchair accessible. I don't know if it truly is, but it's seems close and the park staff does drive a golf cart kind of thing up and down it.
If you go to "reserveamerica.com" (which you need to use to reserve sites within NYS park campgrounds) you will find several places to go. In my experience with our larger 5th wheel, we don't expect to "show up" and get a site without reservations ... but with a tent or smaller camper ... maybe you'd be fine?
We have been to (and recommend):
*Robert H Treman SP - Some sites are kind of close to each other, close to Ithaca, NY, Lots of hiking (walk the gorge trail within the campground and many others in the area), the swimming area (part of the river/creek) is walking distance from campsites (it's a very cold spring fed life-guarded area) many waterfalls and one can't forget ... the wonderful Ithaca Brewery isn't too far down the road! I think most sites are pretty level.
*Fillmore Glen SP - Very similar to Robert H Treman but not as many waterfalls and no Ithaca Brewery. Small town close by for needed supplies, some sites are spread out but most, if not all, don't have much privacy. RV sites are blacktop and pretty level, other sites are grass or gravel and are pretty level as well.
*Watkins Glen SP - Gorge trail hike is way cool, normal swimming pool (not part of the river/creek), last time we were there, there was plenty of privacy between almost every site (that we saw). Sites may, or may not be level - we've had both.
*Sampson SP - We love this place and it's great for bicycles (old Sampson Army base and roads are still there and are being taken back by nature - really cool bike riding! Not much privacy between sites (if any) but the sites are pretty large. Life-guarded swimming on one of the Finger Lakes, still has the original Army base Brig that is now a museum (really cool to see the history of the place!), kayaks, small "Sunfish" sailboats to "bigger" motorboats are on the lake as well.
There are many other state parks (I don't know about private) that might fit your needs as well but we haven't been to them ... yet!
Good luck,
John
johnm
'13 GMC Serria D/A, CC, 4x4
'16 Forest River Vengeance 25V