I agree with CDTraveler that entering a restaurant or bar alone is different for a woman than for a man. It has been that way all my life, and it doesn't seem to me to be any more than marginally less so now than it was ten or twenty years ago.
Bars that don't serve food are perhaps the most awkward places for a woman alone; taking a seat at a bar at a bar/restaurant is less awkward; asking for a table at a restaurant without a bar is the least awkward of the three. It helps if you dress and behave as if you're a business traveler (even if you're not). It helps to have a magazine or book (or these days, smartphone) to browse to avoid looking around and noticing that someone is staring at you.
I don't think it's an issue for women only; I know some men who say they don't like dining out alone, for whatever reasons. I'm just saying that for a variety of reasons of which men might not be aware, popping into a restaurant or especially a bar is often not as carefree and comfortable an experience for a woman who's alone than for a man who's alone.