I can't call it true NY-style, because honestly, I've never eaten pizza in New York. However, I'm familiar with the pizza I used to find in the Philadelphia area (which I refer to as NorthEast Pizza).
If you're looking for something close to that and you're in the HEB area, head down to Napoli's Italian Cafe, located at 3008 W Euless Blvd, Euless. They call their pizza "New York Style" and I bet it's darn close.
The pie slices are large and floppy, just right for folding. The ratio of cheese to sauce is just right, with neither overpowering the other. Sauce is your basic tomato concoction, and without too many spices, like some places do. It still has plenty of flavor though, and compliments the cheese mixture well. A slight dribble of grease will drip off the point when you fold the slice in half, just like it's supposed to. Not a puddle, just a drip. The crust is fairly bland, but nice and puffy and soft. It's the kind of pizza I grew up with, and the best I've found around in this area (I admit I have not tried Broadway yet).
The prices are cheap, cheap, cheap, with the largest (giant 18" pie) costing you $11.95. Not bad, considering the last pizza I bought here was 16", $14.95 and not as good. Toppings are a buck each, and are your basic pizza additions. Sad to say, no meatballs on the list of toppings, but they do have a meatball parm sub, so I may ask if they can slice and add to a pizza.
The place also sells a variety of subs, stromboli, calzone and pasta dishes. They offer cheesecake, cannoli and italian ice for dessert.
If you're over in the MidCities, go check it out.
M-Sat 11am to 10pm
Sun 12pm to 8pm