Having lived here most of my natural-born life, (and all of my un-natural one), here are a few recommends in no particular order:
Take a city tour! There are a number of reputable operators offering a variety of city tours. Good way to quickly get aquainted with and learn a lot about the city.
Stanley Park/Vancouver Aquarium - Lots to see at the aquarium and the park is in such a spectacular setting.
Dinner on top of Grouse Mountain. - If the weather is good the view while dining is incredible. Cable car ride to the top and good restaurant to boot.
Strolling English Bay or Kitsilano - Great place for a nice walk.
Museum of Anthropology @ UBC - If you have some time and N.American Native stuff interests you it is one of the premier museums on this topic in the world.
Drive to Whistler - worth it just for the drive. Even better if you
Ski/Snowboard
Dont miss Granville Island
Take a trip to Victoria aboard BC Ferries. Can be done by car, bus or walk on.
George Riefel Waterfowl Refuge - If Birdwatching is your thing. Very accesible from the city.
As for the city itself - Gastown/Chinatown are interesting areas. Kitsilano is kinda neat too. Visit the Vancouver Museum and the Vancouver Maritime Museum. Capilano Suspension Bridge is good.
If you have some time, excellent small hikes can be done in many areas of Greater Vancouver.
Convert your license and take a small plane from Boundary Bay (CZBB)out to Chilliwack (CYCW), for some pie and coffee. Easy flight with lots of scenery. Pie is good too.
Eat - lots of restaurants. Loads of cheap Sushi. Lots of Seafood.
As for Hotels, havn't really stayed at a lot and some other will be able to offer better insight. The Sylvia is supposed to be quaint and is in a great location. Others can fill in better than I.
There is plenty more that I am forgetting, but this is a kick start anyway.
Rgds,
Splork