As a couple posters mentioned there is nothing wrong with eating alone. Here are a couple things that could help with the anxiety if it bothers you.
Bring a book. It will look like you plan on being there alone, didn't get stood up. It will give the other people context. I have even see people bring a laptop, but that might not fit in a very high end place.
As other people mentioned you could go to a place with communal seating or seating at a bar area.
Wear more business attire. This would give people a social context on why you are there alone.
You could also bring a briefcase or backpack with you that would give context of out of town/business.