My comment about Psirri regarding the choice of a hotel in this area was about the noise and nightlife, otherwise the area is quite safe.
About restaurants.
In Psirri I recommend the restaurant Zampano. http://zampano.gr/. and possibly The Greek Creative Cuisine (which I don't find so creative). In both cases the reservation is preferable.
A little further towards the municipal market of Athens there is the unmissable Karamanlidika https://karamanlidika.gr/
In the market itself there are small simple and inexpensive taverns which offer good food with market products. For example the Aris Tavern.
I'm sure you'll be told "Mani Mani" which is located near the Acropolis Museum. If you want a change, apart from the Mani Mani branch next door for takeout (Dirty Mani) in this district of koukaki I recommend "Seawolf" which is 200 meters further at 35 Dimitrakopoulou street.
Continuing this street about 300 meters to the south you will come across Georg Olimpiou street which is a large pedestrian street full of restaurants frequented by Greek families. If you like grilled meats, the Kalyvas Family Grill is the place to go.
If you like street art and street food, don't be afraid to hang out in the Exarchia district, there are also plenty of very good little restaurants there. But you probably won't have the time.