My first true backpack trip was 11 days solo in the Smokies 5 years ago where I did 5 different "trips" all over the park totaling over 100 miles. Started easier at first since I didn't know what to expect or how my body would hold up. There are so many 1 or 2 night trips you could do there, and just stringing together 2 or 3 to fill what time you have may be easier than 1 longer one. There are only a few trails there that are "tough" (going up Baxter Creek for example) but in general I wouldn't worry about what route you may select if you keep the mileage lower to start.

I partnered up with someone for my first trip to the Rockies the following year since I was again not sure how I'd handle it, and it was much more remote and rugged than the Smokies. Now I'm fine doing 7 day loops solo out there.