I want to visit as many national parks/campgrounds/hiking trails as I can on a cross-country roadtrip and maybe see some sights along the way.

I would be starting in upstate NY, what would be a good itinerary? Any places in particular I should stop at? I see a few of the national parks in the Northeast open in late May which is kind of late for my purposes :(

I would be open to anything in the US/Canada. Hell I will probably stop in Montreal either on my way out or back just for reasons. Ideally I'd like to make a stop near the Blue Ridge Mountains because I have friends out there in NC.