Assuming you are staying in the 41st St area you should be just fine w/o a car.
For breakfast I like Tasti Delite, they have a nice breakfast special and lots of differnt choices of omlets. I am a little disappointed they took the red velvet pancakes off their menu though. They were good.
Beyond by Shemtov is like a pizza store on steroids. Their menu is huge, you could go every day for a week for every meal and get a new thing each time. I especially liked the eggplant parmesean sliders. And for a decadent dessert get the zeppoles. Fried dough with cinnamon and sugar, 1 portion is enough to feed an entire family.
I also really liked House of Dog, next to the chocolate store. I got the Carribean dog there and it was really good.
Be aware that if you are there for yeshiva week any and all of these places will be packed.