I also travel a bit solo, but I really don't enjoy going out for dinner on my own. It is just a bit too formal, and it's either couples, groups, or business people together I find.
So I don't do it anymore. I make sure I stay in a nice hotel with a good breakfast, start out exploring early and stop for coffee on the way. I really do enjoy lunch out though, as I find that much more relaxed and less formal, and often a good way to nod and smile at fellow diners and often chat if that's how it works out.
For dinner I'm not bothered, I won't starve and if there is a cheapo place with no tablecloths like a trattoria, pizza place or something like that, I might try it. Otherwise it's a picnic in my room, which is often very enjoyable after a day walking around!
I'm in my sixties now and still a bit intrepid on the solo travelling front, but I'm not propositioned, chatted up or hassled much anymore now, which is very liberating!
If I do get hassle, I point to my ears and say "I am deaf" in whatever language is spoken, and that sorts that out! Strategies my dears, strategies!