A few times, when travelling by myself for work, I would go out on my own for dinner and sit up at the bar. A couple of those times I wound up striking up a conversation with a person sitting next to me - and before you know it we've been there for hours. One time a guy came up to the bar to place a takeout order to bring home to his wife, so he had a drink while waiting. He ended up chatting with me for like 3 hours, lol. I hate to think what his wife had to say to him when he got home. Another time my taxi driver wanted to take a break and join me for dinner too, so we BSed for a while. Another time, the bartender closed the bar down early and we hung out for a while and had several more drinks off the clock.
For the past 3 months that my boyfriend is here with me, I've been eating out with him like all the time. It's going to be so hard to eat now alone since he's going back to LA. I actually wouldn't know how I'd cope up with it.
If I go out specifically to eat then I'm going to be meeting someone over there too. I would never leave the house to go and eat out if it was just me. However if I'm out in town by myself and get hungry then yeah, of course I'll go and have lunch/dinner alone. As ohiotom said, usually in bars you will end up talking to someone even if you go in to eat by yourself.