Dirt Candy! I'm not a vegetarian but I love love their food.
Izakaya Ten in Chelsea, great sake bar with awesome takoyaki - at least they were awesome after a couple of drinks, I've never had them sober.
Biang! in Flushing
I love pastrami with chopped liver on rye.
Turkey and Cranberry Pie
I could eat 1 pound, maybe 2 if I really had to.
Schnitzel & Things!
Nasi Lemak :-)
Xiao La Jiao (Little Pepper) in Flushing. I hope they reopen soon!
Just a few random places off the top of my head:
Pam Real Thai
Cachapas y Mas (Inwood, Venezuelan food), try the Cachapas (sweet corn cakes) with pernil
Xi'an Famous Foods - spicy Chinese lamb burgers, noodles, soups
Woorijip for cheap and fast (but pre-cooked) Korean food
I would advise against going to Carmine's (sorry simon). I'm from Europe as well and almost any cheap (as well as expensive) Italian restaurant I've been to there has been far superior to Carmines. I mean, they make their Tiramisu with whipped cream and I don't think it contained even a hint of mascarpone, how can you call that stuff still Tiramisu? Unless they have changed 180 degrees since my last visit I would not recommend going there.
Sorry I cannot contribute something more useful here - just wanted to save you from Carmine's.
Thanks for all your suggestions, I'll definitely try some of them. A friend also suggested Minca, they have a variety of pork, chicken and veggie broths and also chicken as a topping.
Just wanted to add this to the list if someone else is interested.