If you only have time for a short ride, just do the park loop. Remember - you must start at Lost Lagoon and head NE as the bike path is a one-way counter-clockwise around the park.
Another option -- take any of the Harbour Ferries across False Creek to make an interesting sidetrip.
It's on MapMyRide. Click on FULL VIEW to see the whole map...
http://www.mapmyride.com/route/ca/bc/vancouver/552123795927859647
If you have more time (and energy) add on the Seaside Bike Path to Jericho and UBC. (see next ride)
If you have more time (and energy) add on the Seaside Bike Path to Jericho and UBC. (see next ride)