Tough to say. It can vary dramatically from area to area. Within the city limits, generally rents are much higher in Yaletown, West End, Kitsilano, Kerrisdale. Lower in Marpole, Joyce-Collingwood, Strathcona, Hastings-Sunrise. Outside the city itself (but still withing the Vancouver metro area) the North Shore is on the more expensive side, whereas cheaper rents can be found in Coquitlam, Surrey, parts of Burnaby and Richmond, and New Westminster. Generally speaking, the further out you go, the cheaper housing costs will be.
It also depends a great deal on the type of rental you're looking for. In the downtown core and in parts of Richmond, Burnaby, New West and North Van luxury high-rise glass & concrete towers predominate. In other cities and less densly populated areas of Vancouver mid-rise apartments are more common. Also very common throughtout the metro are basement and upper suites (where the owner/landlord lives in one level of a private house and rents out a portion (usually with separate entrance/kitchens/utrilities/etc.) For the most part these suites are larger than 1 bedroom so you'd probably be better off concentrating on mid & high rise buildings.
I pay $2500/month for a 1025 sf. 2br/2ba with large balcony on the 25th floor of a highrise in Yaletown. I pay $100/month for an extra parking space (garaged). A 1br/1ba 680 sf in burnably midrise in a fair-to-good area an run from 800-1100.
Good Luck!