People who visit Vancouver are always surprised by how compact the city is. The city has numerous public transportation options from the SkyTrain and the SeaBus provide to vital public transportation options. Here is a transit map to make getting around and understanding the system a little better.
Vancouver is an extremely walkable city. It only takes 40 minutes to walk extreme corner of downtown to the other. You definitely shouldn't spend all your time downtown, though, but even then every neighborhood's within biking distance, some are walkable, and they're never more than 40 minutes away by bus.