My ex-wife is from Vancouver and former sister in law lives on Vancouver Island. I've been there about 6 times. I'm no expert, but these are my favorite places and a few bits of advice:
The Eatery- incredible japanese-indian fusion restaurant. Don't be scared, just go and eat there. It's amazing.
Deserts Falafel- the best falafel ever! There's several locations I believe but I always went to the one on Commercial Drive.
If you're looking for scenery, the drive from Vancouver to Whistler is amazing... plus you'll pass the golf course from Happy Gilmore that they filmed the fight scene with Bob Barker

At night driving through the forests you'll swear there's a sasquatch behind every tree...
You can drive to see Cypress Bowl, it's where they held some of the winter olympics. I got to see the huge jumps and stuff being built in 2009 when I was there.
Lots of provincial parks... hike some trails, the rainforest is totally awesome.
Ocean is freezing!!! Don't swim!! lol.
Can't remember the name of the punk rock club I used to go to, but its a cool place. Something about bricks or stones or something in the name lol.
Lots of pawnshops with cheap gear all over the city.
Taking the ferry from Vancouver to Victoria is a nice little cruise. On Vancouver Island there's tons of small towns with neat little hole-in-the-wall places, so drive up the coast out of Victoria and eat lunch or dinner at one.
I rented a canoe and paddled out across some bay and along a small island in the bay. While in the bay, a seal followed my canoe and repeatedly swam straight at it, only to dive under it at the last second and pop out the other side, turn, and look at me. I could have swore it was smiling. At one point I looked in the water and there were millions of tiny pearlescent jellyfish floating as far as I could see. While canoeing along the coast of the island I saw more bald eagles than I can count. I'm sorry, but I totally don't remember where that was, but it was so awesome.
Stay out of East Van especially after dark. I've seen dudes shooting up in the open during the day, and been asked to purchase drugs just walking down the street. There's a bad heroin problem in Vancouver, just so you know.
If you've never been to Canada, most Canadians are very friendly (unless you talk politics- DONT!!!), the cities are VERY clean so don't litter for any reason, and everything pretty much looks the same, except speeds are in km/h. Have fun!!! Vancouver is awesome!!!