There are soooooo many places.
Since I do not know where in the city you are located, I'll just tell you a couple of my favorite standard places.
These dinner places are not Cheap, but also not very expensive. I don't have tons of money, and I go there!
Dinner:
Steak Frites
near Union Square
9 E. 16th St.
Markt
401 w. 14th St (corner of 9th ave)
get the beef stew!
Bay Leaf
(if you like Indian)
49 W. 56th
between 5/6 Ave
Breakfast:
Bridge Cafe
279 Water St.
(212) 227-3344
The Paris Commune
(get the french toast)
411 Bleeker St between 11th and Bank St)
212-929-0509