Rent a car
Most likely you will need a car rented from Vancouver International Airport and drive it to downtown. But once you are in downtown, a vehicle is not as useful because downtown has lots of one way road, bike lane, and parking is expansive. Downtown is actually about the same size as Stanley Park, so if you can walk around seawall you can walk around downtown without a vehicle. What you can do is to rent it from the Airport and return it in downtown (there is a Budget rental on West Georgia). If there are locations you want to visit not within walking distance, then plan ahead and rent it only for the days you need. For standard vehicles daily rental is $40 plus insurance of $25 a day.
Skytrain and Distance
There is Skytrain running directly from the airport to downtown (which costs $7.95) and from downtown to the airport costs only $2.95. Unlimited day pass costs $10.25
All distance in this site is measured from Downtown at West Georgia and Granville Street.
Bike Rental
Another option is biking. Bike rental is available just around the street corner at $10 per hour. There are bike lanes available throughout downtown.
Parking
Parking costs about $7 an hour in downtown. A parking ticket costs an average of $70 and I have received a ticket (forgetting to pay the meter), after only 5 minutes.