How I did it: Although I love the company of others, I've always preferred eating alone. I rarely speak to others that feel the same way, as most view eating as a communal experience. But I sometimes find that in the company of others, I'm distracted from my food through conversation, and I'll often eat half of my meal before I realize I've barely tasted it. I can't quite remember when I first did this, but I've done it many times and it is gloriously pleasant. If you watch Sex and the City, I think all people (men, too) should watch the episode where Carrie eats at a restaurant for the first time without a book or a newspaper or anything to appear as though she is too interested in another activity to look lonely and pitiful.
You just must remember that anyone that would judge a person for eating alone at a restaurant must be lonely and pitiful enough themselves that they need to seek out others to judge to feel better about their own sordid lives. And just because someone is looking at you as you sit by yourself certainly doesn't mean they are judging you. Perhaps it's someone wondering why such an attractive individual is sitting all alone, and they are pondering how they might approach you to join you for a moment.
And if that's not enough, eating alone announces, perhaps, that you are so terribly popular, that you need a break from all of your social engagements to meet your caloric quota for the day, less you starve to death :-) If anything, it illuminates a beautiful degree of self confidence-- that you know that you are so wonderful, you don't need a "shield" of friends around you to make apparent what a fantastic person you are.
Not to mention, certainly, that people watching is fantastic! ;-) Good luck!