You've picked an excellent location for
affordable public golf. I spent several years there and the golf quality/value ratio is tough to beat. Our buddies trip this past year was in Lexington and I posted some photos and descriptions here -
http://golfclubatlas.com/forum/index.php/topic,45397.0/. A few recommendations are:
1. Kearney Hill - Pete/PB Dye - Several excellent holes and few that are a little shoe horned in, but overall a fun track with variety. 15-18 make for a good finish. The course has been called "Dye light" on the site before. That is probably an apt description with many of his typical features toned down slightly for the scale of the property.
2. Old Silo - Graham Marsh - About 30 minutes east of Lexington it is a very attractive layout. It is cart only though with some severe terrain in places. Bunkering is eye catching, but was in rough shape last year. You may want to call ahead or check with other locals for conditions. That said, if it is even in so-so condition you would enjoy Old Silo.
3. University Club of KY - 36 hole facility with both public and private courses. However, they will allow you to play both for $100. The private course (Big Blue) was renovated by Art Hills around 2001 I believe. He left the routing in tact but redid greens and bunkering. The courses were routed by the original owner when it was the Players Club of Lexington. It is a low key facility with an inviting grill area and well equipped practice facilities. The golf won't change your life, but you'll have an enjoyable day.**There is a newer private facility in town (Keene Run) with the same owner...you may want to inquire about their accessibility.
4. Gibson Bay - This Hurdzan course is an obscene value. I believe the weekday green fee is $14. It is on moderately hilly terrain routed along the hilltops. Again, the course itself will not make the top of anyone's list, but it is one of the best examples I've seen of quality golf that is extremely affordable.
These are just a few suggestions. Some others are Golf Club of the Bluegrass, Cherry Blossom, Peninsula, and Picadome (a charming old school city course built in 1927). If you're looking for private clubs, Idle Hour CC is probably the finest option. Good luck and have a great time!