I don't really feel funny eating alone, but I do get bored very quickly. I'll bring along a book or newspaper so I have something to look at other than my hands. Usually I do try to eat at the bar as they have TV's with some sort of sports to watch. Also, bartenders can be much more chatty than waiters since they are pretty much tethered to that location. While talking to bartenders I sometimes get great tips for other restaurants and things to do while in their city.

By the way, for those who aren't big drinkers, there is nothing wrong with ordering a coke or water while at the bar. The bartenders don't mind as long as you are tipping!