^^^^^^ What he said, Red Rock Canyon is awesome.
The tornado season is basically all of May into June. That's the time when everyone has the TV on in the background tuned to a local TV station.
After the middle of June into July tornado season is pretty much over with, but there is always a possibility of tornados year around.
Oh, and BTW, tornado season means hail season. May through the middle of June is a much higher chance of hail.
I'd have no reservations (no pun intended) exploring Oklahoma until the 1st of May and after the 1st of July.
Oklahoma is a very diverse state, georgraphically speaking. Look up Cross Timbers Of America.
One very interesting place is in the panhandle, the Black Mesa area. If you want some peace and quiet in a beautiful area, go visit Black Mesa. There are not a lot of services there, so be prepared to be stocked up and provisioned. If you are into Astronomy, or ham radio, this is the place to be, it's very dark sky territory as well as low electrical noise.