Yes, have done many times. If you feel out of your comfort zone, have your main meal at lunchtime as it's often more common see solo diners at lunchtime and usually a lot cheaper too, with set price menus. Then you can just have snacks/ light dinner, wine back while chilling back at your hotel/apartment at night.
Would go to a bar solo, if it was warm and had outside seating, somewhere good for people watching. Also if it was not too packed (would feel guilty taking up a table if it was really busy).
As for where to go, I cannot think of many places in Europe, I wouldn't go or that are unfriendly/ hostile to solo travelers. Depends what you like, interests, etc.
I loved Porto, Lisbon nice too, loved Seville, like quite a few French cities, Ljubljana (Slovenia), Munich. If you are flying, I would just look at where is cheap/ easy to get to and then pick a favourite from those options...
If you really don't want to go solo, Meetup.com sometimes has groups who do European city breaks. Not an organised trip or tour, just a way to go to places with other solo travelers and done at cost not as a money making thing..