I would look into the Oklahoma classifieds...You can find many houses just by google OKC houses on the east side. It really is easy because I have been searching myself. The area you are interested in has many trees and rolling hills. Lincoln park golf course near the Armory museum is fantastic...On one of the pars you are looking directly at a armored tank (so cool) great skyline shots of the city also.
Oklahoma City, OK - Oklahoma City Golf
History - Museum - 8k -
The area is called the adventure district... has the Zoo/Remington Park/Oklahoma Science Museum. Great area to live for the countryside of OKC...Really pretty.