Go see some independent Off-Off-Broadway theater for $15-20, close to the cost of a movie ticket. Read the synopsis
Off & Off Off Broadway Shows - Reviews and Tickets - New York Times and pick something with a theme that sounds interesting to you. To make extra sure, do a search on the title of the show to read the bloggers who review it, before you go.
With Off-Off-Broadway, every seat is a good seat close to stage, because the audience must be fewer than 90 or so to be called "off-off-bway" (2 "offs"). Off-Off-Bway is not a location; it's an audience size. Some of the great companies in NYC include Flux Theatre Ensemble, Boomerang, Gideon, Retro Productions and others that put on a few shows each year with a strong company of some Equity, some non-Equity actors. People attend with others, or solo. Seating is often "first come, first serve" so just sit down when the theater opens and read until the play begins. During intermission, stay put. You don't have to socialize at all, just soak in the play and subway home, thinking about it.
Or if you go to a Broadway show, costing more, you're at an advantage to attend solo. When you ask for "best available seating" as a couple, it can be further back. If you ask for just one, they sometimes can fit you into a good row where there's just a gap. Be careful they don't put you behind a post ("Limited View" seating) or way off on the outside aisle. At the box office or online, always study the map of the theater seats before you accept a ticket; there might be several good choices left for just one person. But that's why I prefer Off-off-Broadway where every seat is prime, for a much lower ticket price.