Finding out what's on in Armenia can be frustrating: theatres and clubs often wait until the last minute to advertise, events may postpone openings without notice and locals are notorious for telling you after the fact what a great performance it was and, "why weren't you there?" A little persistence and a bit of asking around will get you the information you want to know.
Yerevan has the most to offer with the greatest variety. Theatres and musicals advertise on the fences around Opera House (Mashtots and Tumanian). Plays, concerts and rock/jazz acts also use handbills and posters, plastering them on kiosks and lamp posts around Opera Square, Yerevan State University and Chess House (Khandjian St.) and along Abovian.
Newspapers list events, but not as many as they should and if you don't read Armenian or Russian, you won't get it (or the time).
Your embassy may have a cultural list for local events--ask at the consulate.
Grapevine: the best way to find out what is on is still the local grapevine, so ask, and ask again. Acquaintances, tour guide, hotel concierge are the starting point, but don't be afraid to ask around.
Artbridge, though incredibly expensive, is a nesting place for one of the in-crowds, and can give tips as well as reviews. Just order the basic coffee to save the budget.
Jerair (Jerry) the owner of Salt Sak/Dolmama on/off Abovian St. knows most of the local gossip and a good deal of art comings and goings. His place will be a stop for most people anyway, so use the chance!
Giumri and Vanadzor
The cultural palace is the starting point, the staff inside are friendly and helpful. Locals are a wealth of information and opinions, even if some of it is dated (that great performance of duduk was last year, but still it was great!).
Start at the cultural palace, the church and then the local hangouts.