I live in North Oak Cliff, so.....
Hugo's is a small seafood place in Bishop Arts with an outstanding cocktail program (two Hugos opened it: one the chef, one the mixologist). We have already been twice. Small, focused menu. Everything is fresh and the execution (cooking or raw) is well done. Definitely recommend.
Pillar in the old Boulevardier space. It's very good food, but for those of us that loved Boulevardier, it just isn't the same. The oyster happy hour will always be missed.
Mayor's House is already a favorite. Turkish food in a beautiful space with actual Turkish staff, most are very good looking.
Jaquval is good and Trades next door is a great sandwich shop too.
Pane Nostro also in Bishop Arts is very good, but basic Italian. It's nothing adventurous, but the pasta is house made, the service is excellent and the atmosphere (especially the patio) is very nice. They moved down from McKinney, I believe.
Cenzo's. For you pizza lovers, this is worth a try. Great, chef driven pizza and amazing sandwiches. Family friendly lawn in a nice neighborhood spot in Winnetka Heights.