There are far too many places to list and everyone has a different preference. Here are 3 places that I like and seem to go at least once while I'm in town. The first 2 are very low key, kind of homey, the 3rd can be impossibly crowded and loud - I guess I'm a creature of habit.
My favorite Italian restaurant IN Little Italy is Benito’s 2 on Mulberry, between Broome and Grand. Where's Benito 1? It's right across the street. But I prefer the low-key family feeling of Benitos 2. BEST dish on the menu - Gamberi Alle Francese, battered shrimp in a delicious lemon/butter sauce. It's served at both restaurants. mmm
My favorite straightforward, reasonably priced ramen joint IN midtown is Menchanko-Tei. There are two locations 43-45 West 55th Street (between 5th and 6th Avenues) and 131 East 45th Street (between Lexington and 3rd Avenues). Take-out is available!
The last place I hate to recommend since everyone goes and the wait to get in is INSANE - Serendipity 3. There are way too many tourists, since it showed up in the movie "Serendipity"... but I'm sentimental and at least once every trip (usually late at night) I end up there. It's located at 225 East 60th Street (between 2nd and 3rd), right around the corner from Bloomingdale's.
A great site Menu Pages Restaurant Search gives reviews and a look at each restaurant's menu.
Strand Books. 18 miles of books... need I say more?
Need some Technicolor wigs, Hello Kitty gear or anything flamboyant and wild? Then visit Patricia Field's Hotel Venus. Located at 302 Bowery (between Blecker and Houston). My favorite past purchases from Venus are a fuzzy apron and mohair pink pig hat combo scarf. Who doesn't need a pig-ear hat combo scarf? There's always something interesting to buy.