I am aware that the nearest city (New Westminster) is developing pretty actively, but there is a deadzone in between the two (Burnaby) that seems to have draconian NIMBY zoning laws. Generally speaking, Vancouver's housing crisis is pretty amazingly interesting and probably is more a result of the incredibly poor transit here[2] than anything else.
[1] There may be some single family units remaining in the Denman neighborhood and there are some remaining in Strathcona (near east van.) as well as lots in Kitsilano and the south shore in general, but both of these areas are generally considered outside of the downtown core.
[2] Oh yea, we have driverless trains, woo... but there are only three transit lines none of which connect to either of our major universities and poor management of the system has left the lines overcapacity.