All of the above suggestions are great! If already at Stanley Park, check out the Aquarium. Also consider biking around the seawall. Tons of shopping in downtown.
If you have a free day/afternoon, check out Steveston in Richmond - it is where Once Upon a Time was filmed - there is a great park area to walk along the water (Garry Point Park), lots of cute stores and places to eat, a big playground/splash park for kids, you can take whale watching tours from the pier, get some great fish & chips... Richmond also has a great Night Market on weekend evenings where you can go experience Asian street market culture and eat an amazing amount of delicious foods. Richmond is also the place to go if you want to try out dim sum.
Beaches are great and there are lots on the west side.
Science World is a lot of fun for kids and is a great one for rainy days especially.
If you have a car, the UBC campus is worth a look, UBC is one of our main universities and it is massive, like a city in itself. There is a botanical garden at UBC with a really cool canopy walk. The Museum of Anthropology is also on or near the UBC campus.