What are some nice restaurants in New York City and Stony Brook area?

Hey guys! So I'll be staying in Stony Brook area for couple weeks with my mom. And I'm planning on going out to NYC. So I was wondering what are some good restaurants near the MET for snack(cupcakes?), lunch, dinner and dessert or great restaurants in the city in general. (But not too pricey) Also if you know, any decent place around Stony Brook or Port Jefferson area. I've been researching online. But I want to hear from locals or who've been there. Thanks! :)