Heartland Shooting Park in Grand Island has regular 3-gun competitions that would be perfect for your AR-15. You can find the match schedule on their website, or it's on the NFOA schedule also. If you want to drive a little further, Eastern Nebraska Gun Club has 3 gun matches also.
If you're looking for more of a traditional High Power target match, ENGC, Lincoln Izaak Walton League, and Fort Kearney Shooting Sports all have CMP High Power matches.
One of the members on here was going to be starting up a training company, but I can't remember who it was. I believe he was an Iraq or Afghanistan vet and had quite a bit of real world experience. Hopefully he'll chime in.