There is a Tinker cycling club. Check out
http://www.tinkercyclingclub.org
There are some trails around. It's a large project that the city is working on.
http://www.okc.gov Click on "Things To Do" at the top and then on the page that comes up click on OKC Trails on the left. Good map of what's done and what the trails will be someday. The completed trails at Hefner, the river and south Grand are pretty nice.
SB