Vancouver is a beautiful city set between snow capped mountains and the sea. If you can see them. The most striking aspect of Vancouver in winter is dampness and fog. The north shore, which you pass on the way to Whistler, is particularly beautiful as iit overlooks water and forested islands.
The Aquarium is an excellent aquarium, with above and below water displays of belugas, sea otters, seals and other marine mammals. The Australian children are the ones singing "Babeeeee beluuuugaaaaa..." It also has large tanks mimicing various habitats of the west coast of Canada. And a rainforest exhibit, with caiman, sloths, scarlet ibis and butterflies. This bit is warm.
Gastown is the equivalent of the Rocks in Sydney. It was a rundown area of town that has been tarted up and converted to tourist traps.
Glanville Island Markets is a market on Glanville Island (counter intuitive I know, but what can you do). It has a range of market type stalls selling everything from complete tat to good stuff.
H R Macmillan Space Centre celebrates Canada's space programme (that's not right). Anyway, regardless of the justification it is an interesting museum and planetarium.
Whale Spotting The waters off Vancouver have many whales, including orca and other species. There are also seals and other marine critters to look at. You may have trouble finding someone to take you out in winter, however.
Shopping for Snow Gear
MEC (Mountain Equipment Co-op) is at 130 West Broadway, Vancouver. It has a large range of all kinds of stuff. You have to join the co-op before you can buy stuff. It costs about $5, and can be done in the shop. MEC
There are several ski and board shops on West 4th St, a few blocks up from the Glanville Island Bridge (whatever its real name is).
Shopping for Other Stuff
Living in cold conditions is part of life in Canada. Clothes and footwear for extreme conditions are not a luxury, so there is no premium payable on them. There are some very good bargains available on warm gear. Canada has Boxing Day sales, which are even better value (although the range of stuff available on sale is severely depleted by early January.) Shopping in shops specialising in workwear is good value.
There is a thing called Pacific Centre in the middle of the CBD that occupies several blocks. It is like any large mall and has shops of every variety, including an outdoors/ski shop and the Hudson Bay Company (universally called "the Bay") which is like Myer or David Jones.
Places to Stay
Rosedale on Robson is a comfortable, apartment style hotel only a few blocks from downtown Vancouver. It is opposite the stadium where the Canucks play, so it can be fun when a home game is on.
Budget Patricia Hotel is cheap, and reasonably central.