As mentioned earlier, waterfront Chios suffered from earthquake damage and was rebuilt without regard for tradition.
Much the same can be said for the plethora of restaurants limani side. Avoiding the more blatant and garish eateries, by choosing to eat where the Greeks themselves eat, will reward you commensurately in your search for traditional Greek Food.
Quay side in the north quarter of the port are two good Ouzeries or liqueur - tsipouro bars serving appetizers or mezedes. Chios is famous for its masticha after dinner liqueur(s), which a make a surprisingly good gift!! You can see different varieties for sale above these locally produced barrels of wine in the photo.
Smack in the center of the Chios Town is the Taverna Dolphins and spot on while waiting for your boat. To the initiated, the Turkish influence may be felt easily, as it is fundamental to traditional Greek cuisine.
For sweets and snacks, the ubiquitous No Name reappears towards the south of the breakwater specializing in dairy-products: yogurts with honey, rice puddings, fried battered Loukoumades drenched with syrup, boxed sweets and more.
A 10 minute walk from the quay, and Chios' oldest restaurant, is Hotzas (Stefanou Tsouri 74). It features locally produced barrel wine and is well worth the walk.
Just by the Public Gardens on Democracy St. is another good taverna. Past the ugly hotels to the quay's south is the Nox or nautical club with delicious unpretentious Greek Dishes!