This isn't QUITE Little Italy, though it
is Chinatown/Lower East Side, so not too far away. Also fair warning: I haven't tried this yet, but have been dying to go for a couple of years (always being whisked away to other places.) If you go, please post a review:
Grotto, a.k.a. Via Monterone
100-b Forsyth, between Broome and Grand
http://www.grotto-nyc.com/
(From the few blocks that constitute Little Italy, walk East on Broome. It's on the west side of Sarah Roosevelt Park.)
Also, this is an old favorite for people who work in the Lower East Side/Chinatown/Little Italy/Soho areas (like I used to), though it's absolutely no frills and more of a destination for its low-key atmosphere and neighborhood feel than for outstanding food:
Sal's Pizzeria and Restaurant
369 Broome Street, between Elizabeth and Mott