Vancouver has an odd, remarkable, and convenient set of transportation options. They provide excellent transportation and are also fun even if you don't have any particular place to go. From a bus or boat or train you get perspectives on the city you might not get otherwise.
Some Suggestions
You can buy a DayPass for $8.00 for adults and $6.00 for children 13 and younger. The pass gives you all day access to city buses, the SeaBus and the SkyTrain. You can buy DayPasses at the SeaBus terminal or at any Safeway, 7/11 Convenience Store, Save On Foods and at many London Drugs and Shoppers' Drug Marts.
The SeaBus terminal is located just east of Canada Place and the Cruise Ship Terminal at Waterfront Station. The SeaBus makes a 15 minute journey across the Burrard Inlet to the Lonsdale Quay Public Market in North Vancouver and back to Waterfront Station every 15 minutes during the day and every 30 minutes in the evening.
The Lonsdale Quay, with its meat and fish stalls, bakeries, delis, fruit stands and small shops, is a destination in its own right. From the Quay, can walk up Lonsdale Avenue, the main street in North Vancouver. Lower Lonsdale, near the Quay, has bakeries, antique stores, restaurants, coffee shops and a bookstore.
If you want to see more of Lonsdale but don't want to walk, remember you have your DayPass so take a bus and explore Lonsdale Avenue shops, visit the public library on 15th, the great London Drugs on 21st, or go swimming at the Lonsdale Indoor Pool at 123 East 23rd Street.
If you want a more nature-oriented adventure, take the #236 bus from the bus terminal just outside the SeaBus terminal at the Lonsdale Quay and visit Capilano Suspension Bridge, Capilano Regional Park and/or the Grouse Mountain SkyRide.
To get back to Vancouver, just retrace your steps. Take the #236 bus back to the bus terminal and the SeaBus back to Vancouver. This trip will take between half a day and a day depending on how much exploration you choose to do.