There is a special place for food in the centre of Thessaloniki. This is the place for meze (the Greek way to say small portions of food, like Spanish tapas) I always think of after a hard day at work.
The New Galerios was actually a traditional place mostly for elderly people to drink their coffee and play cards, but in 2016 they renovated the place and nowadays you can find all kinds of people enjoying their delicious food.
Here you can find both meat and fish at its best! They have a basic menu with some things you can always find in their kitchen and then they also have the daily blackboard menu with all the specials you can find at that particular time.
I would recommend trying their skin potatoes and enjoy them with their home-made tyrokafteri (mashed feta cheese with olive oil and oregano), and if you are lucky don’t miss their fish tartare (most of the times with shi drum). I could actually write down almost everything in their menu because I like all of their food.
Don’t forget about the drinks. Here you can find traditional tsipouro or raki, craft beers, wines and retsina (low quallity wine, which is more popular mostly in Northern Greece).
Depending of how many people you come with, allow for at least about 15€/person if you’re going for a full menu.