Victoria is a small city, so would won't find the same quality of museums and concert halls found in big cities like Toronto and Vancouver. We have one good museum called the Royal BC Museum. There are several small art galleries in the city and throughout the island. This is the website for our symphony. Also, the University of Victoria Symphony puts on several shows a year for cheap prices.
For other types of music and concerts, do250 is a great website to check out for daily and weekly show listings. There are several good music festivals like Rifflandia and Tall Tree which take place in Victoria. We have a small theatre festival called Fringe every year as well as a film festival.