I noticed with myself that I feel intensely awkward dining alone. But if I'm travelling for business, it doesn't bother me: at that point, I have a totally legit reason to be eating by myself.

Then I realized that other diners, strangers, have no way of knowing whether or not I'm out on business or in my own city. After that, I got a lot more comfortable eating alone wherever I am: for all these people know, I could be a travelling businessman or have any of a dozen other "legitimate" reasons to eat alone.

Of course, in actuality, no one there even cares or notices me. But I found having the right mental frame helped it not bother me.

I've also found I get pretty awesome service when I eat by myself, and I get to focus on the food more which is nice. It's peaceful.