I was looking for postings on Nicosia eating to see if I agreed with them, but there were none. So I thought I'd better contribute something.
The Syrian Friendship Club stands out. It's near the US embassy in a backstreet. Get close and ask. I always get lost. A mezze there is an experience (14 cypriot pounds for 2). Dish after dish arrives until you doubt you can do it justice. But nobody expects you to hurry. Vegetarian dishes first. All kinds of dips, beans and potato dishes and salads. The red walnut dip is especially good. This is followed by the meat dishes (actually one platter of kebabs, sausages, and chicken) followed by fruit and a hookah.
Sadly, a great restaurant, Greco's, behind CAARI (Cyprus American Archaeological Research Institute) is now gone. So I won't rhapsodise about the good meals I've had there.
Krystakis' is still there on a corner at Dionysios Solomos Place (Tripoli Gate) serving perfect kebabs with salad. The sheftalia (minced lamb/herbs on a skewer) are a must. As is a table on the sidewalk.
At the Friendship club try to get or take a "village" wine (white) from the Omodos area. They are crystal clear and taste like rainwater after a drought. At Krystakis' it's hard to better a glass of Keo beer with the sheftalia and afterwards a walk down the pedestrian-only Lidras street towards the wall and an ice cream at any of the three ice cream bars (they're all good).