STAGE DOORS OFF BROADWAY
Many of the cast exits from the small off Broadway theaters are through the lobby of the theater, and if you simply hang out in the lobby after you leave the stage area (and keep your eyes open :)), you will be able to catch the actors as they leave. However, when in doubt, an usher or other theater staff member can usually tell you where the cast will exit.
Atlantic Theater Company
Linda Gross Theater
336 W. 20th St., New York, NY
The stage door is at the end of the alley between the church buildings and the actors exit out towards the street. To get to the alley, exit out the door next to the elevator in the lobby and at the top of the staircase leading downstairs. Turn left out of the door and you will see the alley.
Atlantic Stage 2
330 W. 16th St., New York, NY
Cherry Lane Theatre
38 Commerce Street, New York, NY
The actual stage door is to your right as you exit the theater. However, sometimes the actors will exit out through the lobby/front door (Jesse Eisenberg held the door for me as I left :)), or the door of the building up the small staircase to your left as you exit, so I'd recommend just waiting out in front and keep your eyes open as folks leave...
New World Stages
340 West 50th Street New York, NY
There are 5 stages and a large lobby downstairs around the entrances. For some shows, the actors may be outside the stage entrance as you leave. There is also a stage door exit at the back of the theater on W 49th St. (walk across the plaza between 49th & 50th and the back of the building is to your right). I might also suggest you ask stage personnel just to be safe :).
The Public Theatre
425 Lafayette Street New York, NY
This venue has multiple performance areas and the front lobby is likely where the performers will exit. However, it's a large space so keep alert!
NOTE: The Delacorte Theater in Central Park is the venue for the annual Shakespeare in the Park productions (2 different shows per summer, running approximately 3 weeks each). There is no obvious stage door, and my best suggestion is to ask multiple ushers as you enter and at intermission, about the actors you're specifically interested in meeting to see if they know their habits. Otherwise, two sources report that the most common "stage door" is near Gate One on the far right of the theater front. Thanks to my reader Anna for sharing her experience too!!
The Vineyard Theatre
108 E 15th Street New York, NY
The actors generally exit through the downstairs lobby near the stage entrance, and then through the front door of the theater at street level; so no matter where you wait as you exit the theater, you should see them. However, there is an exit downstairs as well, and if they don't ask that you leave that area, you shouldn't miss anyone.