There are no affordable apartments in Vancouver or the region. Sorry.
That said, you can generally choose between close to the downtown and affordable. Safe and decent is a whole different factor, lol.
The West End of downtown and the area directly east of Chinatown sometimes have lower priced units, and neighbourhoods like Strathcona, or along Fraser Street, Commercial Drive or Victoria Drive, but generally the lower cost units are in extremely bad condition or in kinda scary areas. Something to keep in mind; if you have to pay for any transit, you might as well pay for a 2-3 zone (further distance) transit pass, as they're not that much more expensive, and you both save more on rent and often have a faster commute. It can take the same time to commute from an adjacent city as it does to get from the middle of Vancouver up to downtown by transit.
My 'pro-tip' is to look into units along any of the rapid transit routes: SkyTrain lines through/to Richmond, Burnaby, Coquitlam, Surrey or the WestCoast Express commuter train (if the times work for you) to Port Coquitlam, Maple Ridge, Mission will be a fast shot out to (comparatively) cheaper accommodations. Sometimes you can also find cheaper housing on the North Shore (North and West Vancouver), but the transit out there can be iffy.
Sorry, but they're renting windowless closets ("dens") out for $750-$800 Canadian now in Vancouver. It's hopeless, really...