Vancouver has excellent transit, so you can be pretty flexible when choosing a place to live. The cheapest apartments will be further out (New Westminster, Burnaby, Commercial Drive) but if you do choose to live out there, be sure to find a place near a Skytrain station. This will make all the difference.
I lived downtown (in the West End) with two roommates during my first year and paid $725, but it was a cramped living situation. If I was doing it all again, I'd probably find an apartment somewhere along the Canada Line (which goes down Cambie Street). From Cambie, there are express buses that run to UBC along Broadway (9th Ave), 25th Ave, 41st Ave, 49th Ave, and (I believe) 70th Ave/Marine Drive. So almost anywhere along Cambie is convenient to UBC, but it's also very easy to get downtown from there. For me, it was the best of both worlds.