Dinner in the Lower 40's, east side.
If you want something interesting and really good, try Aburiya Kinnosuke http://www.aburiyakinnosuke.com/
It's a Japanese robata place on 45th near 3rd, they have both fish and meat specials for under $20, and it's delicious.
213 E 45th St, New York, NY 10017
For burgers: Rare, Black Shack or 5 Guys.
Not much Mexican, unless for less than 20 you count Chipotle.
Sarge's isn't a bad choice either. Pretty much every good Korean restaurant in Manhattan is available if you're willing to walk a couple blocks south.
320 Lexington Ave, New York, NY 10016