Welcome to Oklahoma. If you head southwest on Interstate 44 you'll get to the Wichita Mountains Wildlife Refuge in a little over an hour. Lots of wildlife - Bison, Elk, Longhorn, Eagles, Prairie Dogs, Birds of all kinds, and lots of rocks.
Just before you enter the Refuge is a small town named Medicine Park. It's an old resort town. I think it was recently voted as one of the most interesting small towns in America. It's an artist haven with several little shops that sell locally crafted items. Of course, it's better to look at this in the spring after the weather has warmed up a little, but the buildings are still interesting at this time of year. Also, just a few miles north is a town named Meers. It has an old general store that is now a restaurant where you can get a buffalo burger. It also has a seismograph machine to measure earthquakes that happen in the area.
If you prefer military equipment, Ft Sill is in the same area. You can get on the base with proper ID (driver's license will work fine) and possibly a search of your car. They have several museums with military artifacts, as well as a "cannon walk" with large guns from most eras.
A little closer to you is the Oklahoma City Bombing Memorial. It's right downtown Oklahoma City. It's very moving, and the Museum is worth it as well. Make sure you get a shot of the Survivor Tree and I like the chain link fence (you'll understand when you see it).
Once the weather warms up, I've always enjoyed the kite boarders and sailboat races on Lake Hefner. They can put on a pretty good show sometimes.
I know most of these are a little far from your location, but it could be good for a day trip. Hope you enjoy the area and find it to be a friendly place to live.