CT to Florida...young snow birds!

My husband and I have made this trip for the past 2 years with our dog, but with the intent of getting from A to B as quick as possible (we only had 4 weeks & wanted as much time in the WARMTH as possible) However, next year we plan to take our time, as our time off has expanded to 2-3 months!!! We are a young couple with a 5 lb dog. We love the outdoors, hiking, trail running, etc. We would love to take our time once we hit North Carolina to look at possible alternate places to rent in the winter months, and to simply see the beauty of places we have yet to see. Just from initial research I am interested in visiting Outer Banks, Hilton Head, Oak Island, Greenville, SC, AshvIlle, SC, Savannah, Ga, Jekyll island, Tybee Island. Looking for the best route and advice on other areas we may want to visit? For cost and convenience with the dog, also looking for nice camp grounds.

Thanks for your help!