Here are a few questions to get you started:
Are you a second-generation millionaire? If so, befriend a member of Camargo and hope they invite you.
If you want a family club with some awesome amenities as well as two 18-hole golf courses, join Kenwood Country Club (KCC) - no tee times is a bonus.
If you want a solid club with a Donald Ross design, go to Hyde Park. Young families and hot moms run that place.
Terrace Park is an inexpensive option. They have a great indoor practice facility as well as a great outdoor short game area.
Oasis (North of 275, Loveland area) is an Arnold Palmer design in a housing complex. I have never played it…most people who join there seem to matriculate to KCC or Hyde Park.
Maketewah might be a little farther from your house than the others on this list, but it is an 18-hole Tom Bendelow/Donald Ross. They just redid their outdoor short game area. It’s pretty sick https://www.youtube.com/watch?v=jiWIuVd_QNg Will Grimmer was/is a member there. As far as cost…I am not sure. I had heard that they slashed their initiation fee, but that was a couple of years ago.
Losantiville Country Club is a great value for an old-school course with practice area. It’s a Tom Bendelow design with some of the best greens in Cincinnati.
Coldstream is probably pretty close to KCC as far as cost and amenities. However, it only has one course. Slope is 140 and stretches just over 7,000 yards from the tips. I have not played in a long time but course conditioning is top-notch.
Cincinnati Country Club is close to Hyde Park and is another old-school course. The guy who owns the Reds has a house just off the fairway (can’t remember which hole) and is next to one of the best private schools in Cincinnati. Traffic can get heavy in that area but it is a place to be seen.
Those are the majority of the courses on your side of town.