I'm a single older woman too. My goto place is the West coast of FLORIDA. Naples is wonderful, rather quiet. still safe and demographically OK. Republican, with a Tea Party group too. I've also enjoyed Sarasota. You could do both on one vacation. I like traveling alone. Found it easy to connect with people in both places, especially Naples.
A lot of info available online. Here's some: http://www.southernliving.com/travel/south-east/florida-west-coast-beaches Also, I really like staying in B&B's. Always someone to talk to , plus owners give good advice on appropriate local attractions. I like the safety of being even loosely connected to locals , just in case.
Actually, I never stayed in a B&B in Naples, so have no specific recommendations. But the more I think about Naples, the more I want to hop on a plane. Really, I love it there.
Thank you, good information. Saw that you have traveled quite a bit. If you have any recommendations in the Naples Sarasota area, I would appreciate it.