Grouse Mountain has a grizzly bear habitat at the top, there is a wolf enclosure located under the Super Skyride near the base.

Walking is a big thing in Vancouver, a few hundred meters to a km or 2 are easy to have to walk depending on when you go, parking can be sparse in many places on the weekend. For Stanley Park, there is a road that circles the park, counter clockwise. On your way to North Vancouver for Grouse & Lynn Canyon take the park drive, you'll see some of the sights and get an idea for what parking is like at different enclaves of the park. As you climb the hill near the Lions Gate Bridge there is an on ramp you take to cross the bridge to North Van. When you come back from North Van, take the first exit after the bridge to get back on the park drive to see Prospect Point and 3rd & 2nd beaches on your way back to the West End.

If the kids like boats you could take the Seabus from Waterfront Stn to Lonsdale Quay, explore a bit then return. Or take a ride on one of the smaller ferries in False Creek to & from Granville Island. If you're staying downtown that would be far less stress than driving across the bridges and gridlock parking on Granville Island.