The New River Gorge for sure. If you want to wait a little longer, go mid October for bridge day. It's the one day a year it's legal to base jump from the bridge. White water rafting as people fell from the sky above is something I'll never forget. The weather that time of year is a crap shoot though. And I recommend the gorge all year round. Just check water levels.

I second the Gorge. It is amazing! Bridge day is a very cool experience and the leaves are absolutely gorgeous that time of year

New River Gorge is a must. You'll want lower New River or upper Gaulley (depending on time of year.) I grew up in WV and this is the best rafting in the country (in my opinion.) I recommend company below. Also, Pipestem state park is amazing if you have time to visit. https://aceraft.com/

I’ve never white water rafted there but I heard it’s amazing.

We used to go to the Youghiogheny River in Pennsylvania, south of Pittsburgh, to whitewater raft and kayak. It’s a fun tiny town.