Longaberger is too far north. As Jason has said, there are too many solid public choices nearby, and I agree with all of them--Shaker Run, Belterra, and Stonelick Hills. Definitely do Shaker Run. The rest are nice, but for public golf, Shaker Run is outstanding architecturally, IMO. I think it is one of the best courses around, and conditions have improved enough lately to visit again. (Do seek out the "original 18" though; the new 9 added to the rotation is not up to par with the first 18 holes. So Lakeside and Woodside, not Meadows). Elks Run is also a decent choice.
There are many excellent private courses in the area if you can get on, with Coldstream being my top choice after Camargo. Golfnow might even have some discounted tee times for several of the public courses. (I'm also a fan of Legendary Run, Blue Ash municipal, and Beavercreek near Dayton, but I have not played them in 10+ years.)