Oh hai there shitty maroon integra
I did a track day last winter on some shitty 8 year old ES100s out of desperation, which isn't exactly an all-season but it's not a track tire either, and it wasn't as terrible as I had feared. Two weeks later I went back on some new Azenis and while I was definitely faster the second time around, it was almost less fun to be on a better tire. More grip means less dodginess and less satisfaction when you pass a 911. That said, I tore those things up. Massive chunking on the edges, huge sections missing on the tread, and they were easy to lock up so I probably didn't do any favors in the flat spotting department. I sold them a week later to some poor bastard to put on his Civic. If you have older all-seasons that might need replacement soon, don't let it hold you back, but I wouldn't tear up a brand new set in a weekend when a proper tire will hold up much better.
If anything, Shenandoah is absolutely brutal on brakes. I've learned to just take it easy so I have something left to drive home on.
I'd recommend Summit Point versus a GT-R hard-park-a-thon. They have awesome karting there so you won't be twiddling your thumbs necessarily, and there's already enough drool-worthy cars registered to make it worth your time wandering around the pits. Hell, between Bobo's Z, my cousin's 335, his mystery friend's Aston, and my hella sweet 21 year old sedan, we've got enough metal to get the ladies wet, if you catch my drift. Or not, but screw it.