If you want to get a good NoMI experience, and you are staying in Traverse City the night you land, I would recommend heading to Arcadia for the late afternoon round, taking advantage of the twilight rates, playing as many holes as you can before dark and driving the hour+ back to TC.
Then, in the AM, hit at least the front nine of High Pointe as a warm up and then head down Highway 72 on your way to Gaylord.
I will agree with Brian, I dont give Arcadia enough credit. I havent played it in at least 5 years and I need to get back out there. Brian, PM me if you'd like to set up a date to play it this summer.
If you can get on Kingsley, it would be worth it for the Thursday AM round. They dont have tee times, the course is never packed and you can scoot around pretty quickly. However, for your first trip to NoMI, Id recommend Arcadia, just so you can experience Lake Michigan and all its splendor.