I lived at PGA Village for 8 years. They have a myriad of membership types. It's a half hour from area noted. The Fox Club is actively seeking members in Palm City. Go play it see if it fits. There are many decent public courses in the general area. A great deal for the summer is the SFPGA membership. Most of the private courses members exit the area and they allow play for nominal fees.
I liked Eagle Creek when I lived there. I thought Twin Rivers was pretty good too. I wanted to play Bay Hill, and Mission Inn, but didn’t get to it. Dubsdread was also on my todo list, and I hear they have an awesome cheeseburger. Finally, Winter Park (Nine Hole) is on Golf Week’s Top Courses you can play.