How fast is your plane? If you have a slower plane like mine, but don't mind a 3 hour trip, or if you have a fast plane, you might try French Lick, Indiana. There are two nice resort hotels, although I would suggest West Baden Springs over the French Lick hotel. They have several nice courses, including one that has hosted PGA Seniors tour events, there is a small casino there, and they run a free shuttle from the resorts out to the local airport and back on demand because the city really values general aviation as a way to get tourists to come.
https://www.frenchlick.com/hotels/westbaden Click the link for golf, and you will see that there is a really nice selection of courses to choose from.
West Baden kind of reminds me of the Greenbrier. It even boasts a sulfur spring. It's not as nice as the Greenbrier, but you did suggest in your post that you are on a budget, right?