NC to CA
I did the reverse of your trip about 14 years ago. Except when I had to make up time, I avoided Interstate roads.
It went something like this:
Shipped bike to CA, did the tourist thing, downtown LA, Hollywood, Rodeo Dr then on to Las Vegas. Went to Hoover Dam, then down to Tombstone AZ, Bisbee,AZ, Deming, NM, El Paso TX, Alpine, TX, Del Rio, TX, San Antonio, TX, Houston, TX, Vicksburg, MS, Tupelo, MS, Cornith, MS, Pulaski, TN, Chattanooga, TN.
Finished the last leg via US 64. Did this in February (probably not smart), as a snow storm went through before me and another was following.
Almost forgot to mention, did this on a CBR 1000
Good luck and have fun.
AMA Charter Life Member # 497915A