Reddit reviews Paddling Eastern North Carolina

Try Eno river state park, right there in Durham. There may be campable spots look into it. There are at least 5 sections that I recall.

cape fear near Lillington has a class 2 run. Upper Haw is class 2.

You don’t need much for rapids for a great canoe trip there are many rivers just finding where you can camp is tricky.

Here is a book on eastern NC:
eastern nc paddling guide