I will arrive in Kunming Changshui Airport at 9:30 PM.

You can take shuttle bus line 1 to West Inn Station and then take a taxi to Jinma and Biji Square. It is one of the most famous shopping district in KM. Then find a nearby hotel to spend the night.
The next morning, you can still take a taxi to West Inn and take the shuttle bus line 1 to the airport. The first bus leaves for the airport at 5:00.

Thanks very much, Antonio. I was thinking more like seeing some historical or cultural sites. I am not into shopping. You have any suggestions along those lines?

Well, according to your arrivial time, it's too late to tour around those historical/cultural sites. These places are closed at that time.Thus, I'm afraid that you can only go to downtown area, taste some local snacks and go shopping.