I can't give a recommendation for Tulsa, but for a traditional (not memory foam) mattress in OKC, I definitely give two thumbs up for Oklahoma Mattress Company, at N.W. 4th and Classen.
Their mattresses are made to order, as firm as you would like, and they are flippable (i.e., they are actually a mattress on BOTH sides, unlike most today).
The same people have owned the company for decades and I sleep well on an Extra Firm.
Their mattress, brand new, was MUCH heavier than my previous one -- which at a dozen years old would supposedly weigh so much more from the dust mites, etc.
I am not a paid endorser, but I like their product.
http://okmattress.com/latex_mattresses_pillows/
This is a big thumbs up for an OKC mattress!! I replaced a high dollar tempurpedic from mattress firm with one of these over a year ago. Very nice indeed. There are some mattress forums somewhere and that is where I discovered OKC mattress