Hi voidray,
I enjoy going out to a restaurant alone but also find it awkward at times. Growing up as an only-child, I learned to enjoy my own company. I have some fond memories of doing things by myself, museums, shopping, long driving trips etc. Sometimes eating alone feels calming and reflective and sometimes it feels lonely. Sometimes I also feel as though everyone is looking at me. These days what I try to keep in mind is that 99% of the time people are thinking about themselves! While I am wondering what that "lady over there is thinking about me," she is probably wondering the same thing. But to answer your question as to whether eating alone seems odd, I really don't think so. People are eating by themselves all over this great nation.

The person at the diner, the person on a business trip, the person who just wants to sit and enjoy their dinner over a newspaper or magazine etc.