Good advice from small H. There are about 10 restaurants on Stone, all of which have outdoor seating. Specifically, the Carvary menu at Ulysses is a great bargan; menu online at 1100 hrs every morning.If you like people watching, this is the place for u.
On the other (Hudson) side of FiDi, you should consider Gigino (Batt & West) which may be too $$ and fancy, but v good. Battery Gardens (Batt Pk) with v forgettable food. Both have two of the best views on the planet. 10 minutes (walking) farther north, PJ Clarke's (you get what the give) has v good outdoor seating. Please let us know what you decide to do and how it all works out.
250 Vesey St, New York, NY 10281
State St and State Plz, New York, NY 10004
Gigino at Wagner Park
20 Battery Pl, New York, NY 10004
Stone St. is a short walk from Battery Park, and there are several restaurants there with outdoor seating. Adrienne's Pizza Bar is pretty good, as is Smorgas Chef. Ulysses has the menu you're looking for, but I've never eaten there (except for oysters during the oyster festival), so I have no idea how the food is.
Adrienne's Pizza Bar
54 Stone St, New York, NY 10004
53 Stone Street, New York, NY 10004
93 Pearl St, New York, NY 10004