Not sure what route your taking...But if coming down 95/85 corridor you're going to pass a few good lakes on the way to Charlotte too....
Gaston and Kerr on the VA/NC line. Gaston is primarily a spotted bass lake now but still has big LM that are more catchable in the spring. Kerr is an amazing lake, primarily LM but last few year the spots have been showing up and right now it's the part of their invasion cycle where you actually catch big ones (I caught several 3 and 4 lbers last season). If the water is high at Kerr its some of the most fun bass fishing you'll find (IMO), flooded brush, shallow fish, power techniques. You could fish both of these lakes if you stay in the area, I'd stay in the Gaston area over the Kerr area, lots of rental houses on the water.
The Raleigh area lakes obviously are known for big fish, Jordan - Falls - Harris. I can't offer any insight on these though. My understanding is that these lakes hold big fish but are tough to figure out.
As to the lakes on your list, Norman is a spotted bass lake...High Rock is a LM lake and probably the best bet of what you listed at a big LM, though not the easiest to figure out (for me anyway , but obviously I'm not local to it so I only have a handful of days on it). Don't know Badin, but have heard good things, also LM only I believe.
Hope you enjoy your trip to the area, I'd say if you're going to be in the area you should try to catch a spot, they are super fun...Like smallmouth but angrier .