The city's two major museums -- the Archaeological Museum and the Museum of Byzantine Culture -- are handily located side by side near the fairgrounds. Decide whether you'd rather see gold from the tomb of Philip of Macedon, or images of life in Byzantine Thessaloniki, and be the first one through the door at the museum you choose. After visiting the museums, stroll back along the harbor past the White Tower to the center of town for lunch. If you feel more energetic, hop a bus or take a taxi to the Upper City (Ano Poli), have lunch (perhaps at Tsinari's Ouzeri), and stroll downhill. Reminder: Most of the churches you want to see here are closed in midafternoon.
After a nap, you might visit some of the Roman monuments and the churches of Ayia Sofia and Ayios Dimitrios in the city center, keeping in mind that plenty of cafes are nearby, as well as the famous sweet shop Terkenlis in Ayia Sofia Square. When you're ready for dinner, head to one of the cheek-by-jowl restaurants in the Ladadika, the restored warehouse district which takes its name from the olives and olive oil once stored here. Another not-to-be-missed dinner choice is the justly famous Thanasis, in the rambling Modiano Market.
Note: This makes for a very full day, and you'll certainly enjoy Thessaloniki a lot more if you have more than a day here. Byzantine churches take time to find, to see, and to enjoy. Many of the frescoes and mosaics are high up on walls, or faded by time (be sure to bring a strong flashlight).