Actors Shakespeare Project has a program working with teens. This weekend, those teens will be putting on a production of Henry V in Chelsea Charlestown, near Sullivan Square, free but needing reservation (directions at the link).
The venue is depressingly squalid, the production values are almost non-existent, and the material is certainly not Shakespeare's best. But it turns out that none of that is actually required for theatrical magic to happen. The show was really excellent, despite, or perhaps to some extent because of, its limitations.