It’s a question the New York Chowhound gets all the time: "Where’s a great place to eat outside?" The most recent inquiry comes from edub, who specifically seeks brunch. (The answer: Locanda Verde, which takes reservations.) Here’s a handy collection of threads on the topic. Although the highly recommended Le Jardin Bistro is closed, for an outdoor French fix one might try Gascogne in Chelsea or Resto Leon in the East Village. RGR even suggests Shake Shack, which would be quite a way to start a day in the city ... or ensure a trip straight back to your hotel or apartment for a nap!
As for a romantic patio in Little Italy, most hounds are convinced such a thing does not exist. Beau711 goes so far as to say, "Fuhgetaboutit!," so it’s probably best to look elsewhere in these threads for your patio/sidewalk/garden dining needs.
Locanda Verde [Tribeca]
377 Greenwich Street, Manhattan
158 Eighth Avenue, Manhattan
Resto Leon [East Village]
351 E. 12th Street, Manhattan
Shake Shack [Flatiron]
In Madison Square Park, Madison Avenue and E. 23rd Street, Manhattan