Recommendations would be appreciated. Dine at the bar?
Dining at the bar is not at all common in Greece.
I kinda think it's not particularly common anywhere in Europe.
It's something I do often here in the US, though.
I was in Athens this spring with a Rick Steves Tour and I didn’t have any trouble eating solo in any restaurant I wanted to try. Some of my favorite restaurants include the Peacock Bar & Restaurant on the roof of Hotel Hera, God’s Restaurant, and To Kati Allo. Least favorite meal was at Xenious Zeus; it had a nice view but I thought the food was terrible.
Never had any issues dining as a single woman in Athens and never felt I was out of place. I found the Plaka area was good for my preferred casual-style meals.
I am a male but also a solo traveler/diner.
At first it may be a bit uncomfortable but it's not rare to see other diners eating by themselves for what ever reason.
I never noticed any issues with a single person eating at the bar but never really thought about it either.
Sit where ever you'll feel comfortable and the food will make you feel less self conscious. A glass of wine will help!