Spitzer's Corner with a really good beer selection and Alias on Clinton Street both have good burgers with good meat.
Back Forty in Alphabet City has a really great burger and their list of mostly all local beer would be perfect.
Ruby's is very close and has a notable burger.
Meatball Shop essentially sells meatball sliders.
Little Giant isn't bad, and worth mentioning, though it's cramped.
I wasn't impressed with the meat at Schiller's or Royale, personally. Neither really felt like a substantial meal to me.
Fat Radish. Their burger is delicious, perfectly cooked, with intelligent bun design that allows you to actually eat the thing like a burger without unhinging you jaw. It's technically in the LES, though the cross street is Canal. It's maybe a little hipstery / sceney, bu I liked it as a date place. They have Sixpoint on tap, so it's good for beer too.
For a less fancy place but equally good beer and burger, I could recommend to Black Iron Burger in the East Village. It's dive-y, so it may not be what you want for a "nice date night" (depending on the date), but the burger is as good as Royale's and the beer on tap is better.
Another option in the East Village would be Back Forty. More casual than Fat Radish, but still fully acceptable for a nice date, equally excellent burger, good beer list.
I would recommend against Spitzer's, though they have a very good beer list and are right in the heart of the LES. The burger is maddeningly inconsistent.
157 Ave C, New York, NY 10009
190 Avenue B, New York, NY 10009
Black Iron Burger Shop
540 E 5th St, New York, NY 10009
17 Orchard St, New York, NY 10002