During its history, Thessaloniki was protected by city Walls. In the location where Vardaris Square (or Democracy Square) currently is, the West Gate of the city used to exist. In that area the main streets of the city (Egnatia, Monastiriou, Lagada, Leoforos Nikis, Dodekanisou), were crossing and they still do but of course many things have changed since that times.
During Roman times this was the area where the Byzantine avenue was passing. This avenue currently exists below Egnatia Street and a small part of it has been revealed in recent years after excavations that took place for the constructions of the city’s metro. The part of the Byzantine avenue that has been revealed is at the intersection of Egnatia and Venizelou streets. If you happen to pass from there during the day you will be able to see a part of it.
Vardaris square at some stage in Thessaloniki’s history used to be the centre of the city with most of the shopping activity taking place there. Nowadays, the city centre has moved Easter and reaches even until the White Tower of Thessaloniki.
If you would like to see the part of the West Walls of the city that has been saved it would be nice to visit the area and perhaps combine it with a visit to the Trains Museum or the Insectopia Exhibition or even the Church of the Holy Apostles (unesco monument) that are located relatively close to Vardaris Square.