Not really a lot to add to this at this point as most have struck things pretty well. On this board, I think it is pretty likely most will prefer a "golf-centric" club with a quality course. I think that is a given.
Having a wife and a 7 year old girl, I may be one of the few that feels a pool may be important at this point in time.
Also, I would like to see some sort of junior program, which I believe some may be overlooking as important. In this day and time, when memberships are down, it is partially because the older generation who grew up on country clubs are dying off and not really being replaced by the young golfer. In order to keep our clubs and courses going, the younger generation (of not just high level golfers) needs to continue to be cultivated.
Due to my current and future family composition, I guess I might be a little more interested in the "country club" atmosphere to give them things to do in order for my golfing addiction to be more feasible to them. I guess that is part of why I decided to be on the board at my club, because we are kind of in line with what everyone else here is saying they want. We have a fun golf course, that has a regular game with good players. Everything is geared to the golf side. We have a small kitchen that makes sandwiches, burgers, dogs, chicken, etc and an excellent cook on the outside grill as well. Things are mostly pretty inexpensive out there. It is semi-private so tee times are a necessity, but I wouldnt call it difficult at all for members to get tee times.
Perhaps the main thing we lack that might be nice is a strong practice facility. We have a small range and putting green, but they mostly get the job done for me. I'm more a guy that practices on the course by myself, so its not a major deal to me.
Now left to my own devices I think the perfect club for me within reason of where I live would be the University Club on the outskirts of Lexington, Ky. If I lived closer to there, it would be perfect for many of us on this board. It is a golf only club with a small kitchen and bar. No pool or tennis. They are the home of the UK golf teams, so they have excellent practice facilities and 36 very good holes of golf, to give plenty of variety and options. I believe they are pretty fairly priced as well for memberships. At one time, they had 18 holes that was open to all and 18 holes reserved for member only play. This also makes for a great way to accept outside outings on any day to make that extra cash, but still be accessible for members. They seem to have the perfect model for the golf only member.