I grew up in Vancouver so I thought I'd offer a few tips.
1. Despite what others have said in this forum, public transit in Vancouver is TERRIBLE. I can say this because I've travelled extensively and have lived in various cities in North America and Europe. So if you don't have a car and want to avoid long commutes, try to live near one of the major transit corridors. Also consider cycling if you're going to UBC.
2. For people planning to attend UBC, the West Side of Vancouver is beautiful but expensive, so allocate lots of time for apartment hunting. I wouldn't recommend cycling from Burnaby, but Richmond is perhaps doable if you don't mind a bridge. There are express buses up and down Granville st., so connections from the downtown/West End areas are fairly easy, as are Skytrain connections on the Canada line. Millennium line and Expo line routes will take longer; they seem direct, but once you're on that long bus ride on the 99 you'll wish you lived closer. If you don't like commutes but don't want to pay Point Grey/Kitsilano/Dunbar prices, look in South Vancouver -- Marpole, for instance -- or further east towards Cambie or Quebec st. You can probably go as far east as Main without TOO much discomfort, but further than that and you're looking at a very tiring commute. Richmond is close if you're ok with suburbs.
3. For people heading up to SFU I'd heavily favour the Hastings-Sunrise, Commercial Drive, or Main st. areas. New West, Burnaby, or Coquitlam will wear you down if you enjoy more urban environments, and truthfully aren't much less expensive. Hastings-Sunrise/PNE would probably be my first pick since you can take the 135 express bus straight up the mountain (I'd say about 30 mins from Hastings & Nanaimo). It's an up-and-coming neighbourhood with lots of great eateries (check out the Red Wagon diner, Roma, and Moccia's deli, for starts). There are many nice houses to be found between Hastings and Renfrew or north of Hastings toward the inlet. Many were built between 1910 and 1945 and offer reasonable rents for a partial house. Strathcona is also close to the 135 route and offers a nice community in one of Vancouver's oldest neighbourhoods. However, nice houses/apartments in this area are scarcely on the rental market; people tend to nab them and hold on for a long time. If you really must live in Burnaby, look around Deer Lake.
4. Vancouver really is an outdoorsy city. It's not as culturally interesting as Seattle, Montreal or Toronto and not even in the same league as SF, NY, or Chicago, but the surroundings are incredible. I miss them almost every day.
5. There are no truly dangerous areas in Greater Vancouver. Even in the downtown eastside you're probably more of a threat (esp. in a car) to the addicts than they are to you. Still, don't live there.
