If you want to do something solo and not involve meeting other people, just hit the beaches. CA, FL, even the outer banks in NC. Tampa, FL is cheaper than Miami and more family oriented/laid back. I love Miami though and there are lots of cheap hotels. Or you could visit a friend.
If I were planning on an introverted solo vacation, I would pick a place that either I was interested in potentially moving to to scope it out OR I would do something where the weather and scenery were lovely and all I had to do is walk outside to feel like I'm on vacation.
If you want to be real incognito, pick a less popular town that has even cheaper rates for food and lodging.