As a very rough guide if you think about the sticky out bit of Side facing the sea (where the harbour is etc) then the beach to your right is the holiday beach. Many of the restaurants on that side would be at least partially geared to holiday makers tastes. The beach to your left is the locals beach and the restaurants in that direction are more likely to serve dishes to suit the locals.
We did find one restaurant which can be reached from the ruins at the end of the sticky out bit, next to the big night club, which has a wonderful view of the ruins but we only had a few cold drinks there. It might be worth a try if you can find it.
I hope you enjoy your visit to Side.