I have played two Norman courses: The Golf Club at the Ritz Carlton in Orlando and Elks Run outside of Cincinnati.
The Ritz Carlton course is non-distinct and falls into that nebulous category of "typical Florida resort course." A good deal of water, relatively flat, expensive in season and virtually forgettable once you leave the premises.
Elks Run is interesting and well worth a play in my opinion. The two nines are quite different: the front nine has decent width and has the more interesting holes. The short par four seventh (with a creek bisecting the hole in front of and to the right of the green) is well done. The drop-shot par three eight is very well done and has a great sphincter tightening factor due to the elevation change and the penalty for missing the green (a pot bunker in front, a severe drop off to the right and a run-off to the back). The back nine is tighter (many more trees as the front nine is done in a more faux links style) and more penal. It makes use of a creek that meanders through that portion of the property and several greensites are located just on the other side of the water. The back nine is a bit contrived and a bit too difficult for my tastes but the front is fun and fairly solid. In recent years, the golf course has gone through some rough financial sledding. The original owner, who viewed it as a true country club for a day (pay one green fee and play all day), went bankrupt. The owners who have it currently have struggled with conditioning (a brutal summer in Southern Ohio last year was particularly hard on the course). The other issue is that relatively close by is Stonelick Hills (designed by the owner and pretty well done for an amateur) which is well conditioned and, from what I see, preferred by players who are choosing between the two.