The famous White Tower, near the waterfront, dates from the period of Venetian rule (1423-1430). You can’t miss it. However, if you don’t take the time to wander around the city it’s easy to miss a lot.
The best thing you can do in Thessaloniki is to get lost. Wander around anywhere above Aghiou Dimitriou St and look at the city walls. Not just what they were, but how they are intergrated into the life of they city. Some places treat their historical monuments as something separate, removed. Not here.
A bit of background - the first walls were built when the city was founded, but have been continually extended and reinforced. Some of the walls in Ano Poli, the upper city, were first built in the first century BC, but have been repaired and rebuilt many times since then, often with recycled materials. The fortifications at Vardar, for example, used the marble from the old hippodrome. Most of what we can see today is from the Byzantine era. Large sections were demolished in 1869, but a lot remains.
What I think is most striking is the way ancient and modern are juxtaposed..
The walls are not a monument, they are a part of a living breathing city which is in harmony with the past. In these photos you can see how people live with the walls as part of their lives, even part of their houses.
For the most part, the medieval walls of the city still stand, as well as remains of the older Roman and Hellenistic ones: something you don't see often in other cities.
The east wall runs upward almost directly from the sea starting with Vardari fortress. A good place to start is the Golden Gate on Egnatia (near it's junction with 28 Oktovriou st.).