East Lake itself is a golf club, not a country club -- at least in its current state. I don't know if it's always been that way, but they have no amenities beyond the golf course itself (no tennis courts, no swimming pool) and they don't even serve dinner.
But East Lake isn't that great (again, in its current state... no idea what it was like before Rees Jones). I enjoyed playing there, but I've played a lot of courses I think are better even in my limited experience (mainly the southeastern US).