I've lived/worked in Ga and Fla. Both pay about the same for RN's ($22/hr and up depending on degree/experience/where you work/hours..) I don't know about LVN/LPN's. The further south you go in Ga or Fla the more hot/humid the weather will be - same w/SC but overall summer is summer and the heat/humidity are part of it.
I don't know about employment in SC but in Fla there seemed to be more opportunities outside the larger cities than in here GA but in in ATL (I don't live near there) opportunities seem plentiful - at least in the paper/job sites/facility sites.
You would need, at least in GA and FLA you license for either state first in order to get interviewed/hired I would think. Most places won't consider a nurse w/o the nurse living in the area and licensed - with the exception of the Federal Gov't. As long as you have a current license (LPN or RN) in any state they will look to hire you. www.usajobs.gov
and I know they do offer employment to nurses in one state who are seeking to go to another.
If you don't plan on relocating until after your get your BSN you have a ways to go and a lot can change by then.
As far as gay community...never saw any issues for the gay/lesbian couples I knew in Florida but that was close to Jacksonville. ATL has a large gay/lesbian population and I know the Athens, Ga area does as well. As far as SC, I don't know.