I grew up in Broken Arrow but didn't ride much then. Most of the riding I did was on nearly deserted roads outside of town. I'd stay clear of the downtown area or just north. SE side is nice, all the surburbs are OK but I'd say Broken Arrow is probably best. My brother still lives there and likes it. It's typical midwest...boring and quiet for the most part.
As far as tracks, there's Hallett Raceway west of Tulsa maybe 30 miles or so. My favorite track in the area, better than Heartland Park (Topeka, KS), or MAM (Omaha). They have very laid back track days, you basically e-mail and tell them if you want to ride, pay when/if you show up. They run CCW and CW sometimes, CW not having great runoff areas in a couple spots though.