Unfortunately, Oklahoma pretty much sucks for trout on the fly. Like others have said, they put stocker rainbows in some of the lakes during the winter months. Blue River near Sulphur (about 1.5 hrs S. of OKC) gets stocked in the winter. Lower Mountain Fork around Broken Bow (far SE corner of the state) has a year round population. And you can catch them below the dam at Tenkiller (S. of Tulsa). I'm not sure if that's a year round fishery or not.
But, if your quarry is wider than trout, there are plenty of warmwater fisheries all over the state. IMO, bass on the fly beats trout every day and twice on Sunday. I don't think you'd have to work too hard to find a farm pond around Stillwater you could get access to. A 6 weight rod (you could probably get by with a 5), a white or chartreuse popper and a black Clouser, and a float tube (if you have one) will get you into plenty of bass (along with bluegill, crappie, catfish, etc. depending on the fishery) on any pond or lake in Oklahoma.