If it was up to me, I would play Hornet's Nest, Bradford, and Eastway. Hornet's Nest, IMO, is one of the best public's in NC. It's both challenging and fun, plus you can play either the Nest or Web layout. Bradford has a good variety of open and wooded holes, plus a couple of holes play around a pond. Eastway just because it's a good change of pace from the other two. It's very open and there are many opportunities to show off the big arm.
As for the other three, Bailey Road is very short and easy. You could use it for a warm up. Nevin is very challenging. Definitely have to hit your lines here. Playing it feels more like a chore than anything. I've never played Sugaw but have heard it's good.
I also recommend considering RL Smith and Idlewild. RL Smith's a brutal workout but has some fun holes. Idlewild is just a beautiful, wooded course. It also has a couple of water carriers (try not to lose your disc on hole 9, if you play the longs)
I hope this helps. Either way, you can't go wrong spending your whole day in Charlotte slinging the plastic.:thmbup: