Check with one of the hotels near the terminal like the Pan Pacific to see if they will check your bags for you.
There are tour companies that offer day trips around Vancouver but the downtown area is easy to explore on your own.
If its raining you may want to look into the tours.
First head off to Stanley Park which is about a mile west of the downtown terminal. There is a great aquarium there if you are into that.
A few blocks east of the terminal is Gastown where there are some interesting shops and places for lunch.
The best shopping area is around Robson Street starting at Pacific Centre Mall and then going west.
Vancouver has a lot of great restaurants so do an internet search on the kind you like.
I would wait until after rush hour to leave for the airport so have dinner downtown and then head out about 8:00 - 8:30 pm which will give you lots of time to check in for your flight and enjoy some of the shops and sights at the airport.
February 1998 - HAL Westerdam E. Caribbean
January 2000 - Carnival Ecstasy - Mexican Riviera
February 2002 - Costa Atlantica - W. Caribbean
February 2004 - Grand Princess - W. Caribbean
March 2007 - RCI Voyager of the Seas - E. Caribbean
May 2007 - RCI Voyager of the Seas - Western Mediterranean (Mrs. E. & daughter only - I had a medical emergency)
October 2007 - RCI Adventure of the Seas - Southern Caribbean