I recommend you rent a bike someone on the seawall, it runs through many must see Vancouver attractions. Maybe rent a bike at the Convention Centre, that way you'll get to see in order Gastown, Canada Place, Coal Harbour, Stanley Park, English Bay, Yaletown, Science world, Olympic Village, Granville Island, and Vanier Park. If you spend enough time at each location, you probably won't be able to finish the entire bike ride though.
Lynn Canyon is quite pretty to visit too if you want a small taste of what BC has to offer in terms of nature. Lynn Canyon has a suspension bridge as well, so that will save you the cost of having to see the Capilano Suspension Bridge (IMHO is overpriced and underwhelming). Maybe hike the Grouse Grind if you are into hiking, the Canucks prospects do it every year.
You should also visit Commercial Drive (aka The Strip) for food, there are a lot of good eateries along this street, check out La Mezcaleria, it has great Mexican food and a good atmosphere. Dolce Amore a block down from there has great Gelato as well, definitely worth checking out.