Having grown up in Tulsa, I can tell you where I have been herping. I lived near the 41st/Riverside area growing up (think 1970's-80's) so I spent a lot of time at the Arkansas river. Garters, water snakes, rough green, racers were all caught around there.
It is getting harder to find places. I've had good luck going out to public hunting areas during the off seasons to flip rocks, especially around Oologah lake and Keystone lake. Technically, you need a reptile collectors permit to do that. You can go to
Oklahoma Department of Wildlife Conservation and find that in the regs. I've never been stopped though. Ymmv. The best for me has been just asking friends who may own some land to see if they'd mind me collecting snakes on their property. Very few have ever said "no".
Good luck, and post pics if you go!