If you are looking for a general schooling show, NEOSHA (a small organization in OK) puts on shows almost every month in different areas throughout the state, although mainly in Norman. They have over fences classes and flat classes at a decent price and wouldn't be a long drive. If it's in Norman, it's an indoor arena with a field to w/u in. The arena is kinda small but your horse is exposed to a lot of new things in a safe environment. I used to take young horses all the time to get them out and about and older horses to school on them.
There used to be small random 4-h shows all over the place if you just wanted to get out and do some flat classes. If you want OF, you pretty much have to go to the H/J associations mentioned above or to the NEOSHA shows. Here's their website www.neosha.com and they do have prize lists and scheduels available