A good place to start is The Georgia Straight– Vancouvers equivalent of Time Out. It has listings for Film, Theatre, Gallery, Music and Club events.
The Arts Club is Vancouvers most mainstream Theatre group. It runs shows in 3 theatres the biggest in a converted cinema on Granville St close to Broadway and the other 2 on Granville Island. Subject matter and quality varies.
There is an active Comedy and Improv group on Granville Island. Its not in the same league as Chicago’s Second City, but its often good for a laugh.
Big shows come to the Queen Elizabeth Theatre
Bard on the Beach is a uniquely Vancouver event Shakespeare plays under canvas on English Bay theatre doesn’t get better than this. But if you want to attend, the season ends in September but it starts in June with open (cheaper) previews.
Because Vancouver is a major film production center (Hollywood North) the amateur dramatice scene is very active. The United Players who perform at a small venue near Jericho Beach is close to UBC.
There are many small Community Centres all around Vancouver producing a very varied range of plays, much cheaper than the mainstream theatres and often but not always of a very high standard. Check the Georgia Straight for listings.
The Cultch in East Vancouver often runs eclectic shows . The Havana Theatre on Commercial produces some unusual shows in a tiny venue.
The FringeFestival – Sep 10-20th – so its over for this year – is centred in venues on Granville Island is a small microcosm of the Edinburgh Festival and worth cherry picking events for as is the Push Festival a more way-out version in January just in time to chase the winter blues.
The Vancouver International Film Festival is soon to be underway and finishes mid October. You can check out the schedule at VIFF
The Culture Crawl November 19-22 2015 is an annual 4-day visual arts, design and crafts festival. This event involves more than 20,000 people visiting artists in their studios in the area bounded by Main Street and Victoria Drive north of First Avenue in Vancouver, Canada. Dont miss this one.