Perhaps this has changed since the last time I checked, but at that point, there weren't any specifically. There are theaters like The Beacon and Howland, but those are used for many different purposes (like concerts and such) and not necessarily theatrical performance. I know stage actors who live in Beacon, but I never saw them perform there, that much I know.
There are theatre companies up near Poughkeepsie; for example, the County Players are located in Wappingers Falls. That's just one example of several. If Beacon has any now that I wasn't aware of, please feel free to correct me.
