I grew up playing muni/public golf on Long Island, and I am generally happy to play golf just about anywhere. However, while living in North County San Diego (2005 - 2009), I joined a private club for the first time. The reasons why I chose to join a club (and the specific club itself), in rough order of importance were:
1 - Meeting people (establishing regular playing partners) - new to the area, I wanted to get to know some local guys, join a group, etc so I could have a regular game with golfers whose company I enjoy. I joined a golf only club with relatively low frills (and had played there several times before joining), so I felt comfortable I would get along well with much of the membership.
2 - Tee Time Availability & Pace of Play - As I got busier with work and started a family, I wanted to know I could tee off early most Saturdays and Sundays (maybe have a drink or two with the boys afterwards) and still have part of my day for other priorities.
3 - Course quality and reciprocal play - I wanted a quality course as a home base - one that offered variety, could be fun from different sets of tees, etc...but I did not want to play all of my golf in one place, so when I discovered the many clubs (local and elsewhere) at which our head pro could/would arrange an occasional game, I was sold.
4 - Affordability - I would not be truthful if I omitted the significance the reduced initiation (it eventually went to $0 at this club) played in my final decision. I was pretty young when I joined, and could have afforded a bit more, but felt this club offered a strong "bang for the buck." The dues and other fees were not too bad, particularly (in my view) because I could play year round.
Living in Columbus, OH now, I am faced with a similar decision, and I expect it to go similarly. Course quality will probably get a higher weighting this time around (as I have learned more in the past few years about what I do and don’t like about course architecture) and affordability a bit lower weighting. Lucky for me, there are many great options in the area, even outside the biggest names.