Not sure about your preferred vibe or price point. But to avoid tourist trap places, one generally should venture over to the Hell's Kitchen neighborhood.
I will second the mention of Bettibar (2nd floor above Hourglass Tavern) if you can get a spot. It's very very tiny so can fill up quickly. But its hidden away so provides a nice escape.
West Bank Cafe is great too. The bartenders make a mean martini, and make sure to gorge yourself on risotto balls.
Marseille has delicious french food and great cocktails. Next door to that is Nizza, a nice little Italian place. Both provide great food without completely breaking the bank.
Empanada Mama reopened in a huge space with actually places to sit now and a bar. It is not fancy, but they have the best empanadas you will ever have.
For Mexican food, I always love Arriba Arriba. Very casual, great margs, love their enchiladas. They unfortunately dont take reservations, so weekends can be a little crazy with waits. If you want Mexican that's not as casual and takes reservations I'd go with Hell's Kitchen or El Centro.
Qi moved over to 9th avenue in a nice new space. Affordable and tasty Thai food.
Heading over to 10th ave and 44th, The Marshal is a cozy little farm to table spot. Everything is to die for. It's a couple doors down from 44 & X, which is another great spot (good for brunch) with fun Broadway diva themed cocktails.
Updated On: 1/3/20 at 12:33 PM