hey Milly, I read about your trip today and as I went to Vancouver in February, I have a few ideas of where to go.
1) Take a trip across to Victoria, it is a beautiful place, especially around the harbour. There are 6 Travellers Inns around doing brilliant rates, downtown Travellers Inn is on the corner of Chatham and Douglas I think. Bargain. Also have coffee and cake at Grabba Jabba.
2) Take a couple of days out to look around Seattle, I took the Quick Shuttle bus that picks up where you want pretty much in central Vancouver and takes about 6 hours to get to Seattle. Return was just over $52 US. Call 604 940 4428 for bookings. Go to Pike Place Market on the waterfront for all the great market stands.
3) Take a bus across to North Vancouver and Horseshoe Bay (it was No 250 when I went) and get dropped off at Lighthouse Park. It is forest-covered peninsula with loads of trails that come out on gorgeous rocky outcrops looking into Horsehoe bay and on to Vancouver Island. Nicest thing was that I spent the afternoon there and almost had it to myself, weird really as Vancouver is just around the corner. Beautiful place where you can sit and take it all in.
4) Don't even think of missing one of the crepe cafe's on Robson street, excellent food, loads of fillings and great people. Go for Banana and Chocolate.
5) Walk all the way around Stanley Park, just because it's really nice.
6) If you get a nice day (when the mountains behind North Vancouver are clear of cloud) and take a bus up to Capilano Canyon. From there take the cablecar up to Grouse Mountain. The cloud for me, however did not budge so I saw nothing. Hopefully you'll get lucky and will be able to see all over Vancouver.
7) Get hold of Lonely Planet guides-even if you forget everything else.
8) Check with locals and various drivers on what rate you should pay for a cab before committing yourself, or you may get stung. Hope that you have a fantastic time and take pictures of everything and buy loads of souvenirs if you've got room to carry them.