Car free day is when a half dozen neighborhoods shut down arterial streets for a party! This creates crazy gridlock when people are trying to get around. Davie and Denman are typically the roads closed, but it also messes up adjacent roads like Burrard, Thurlow, Robson and Georgia. Don't have exact details for 2015 yet, just the date.
http://www.carfreevancouver.org/locations/west-end/
http://en.wikipedia.org/wiki/Car_Free_Day_Vancouver
Anyone who's been to Vancouver in recent years will notice countless bike lanes have been introduced downtown with turning restrictions. Cab drivers may look like they are long hauling you, but they are trying to stay legal. Don't get me started about the last Friday evening of each month known as Critical Mass... If you are a cyclist... come to Vancouver for the last Friday to really explore the city.
https://www.google.ca/search?q=critical+mass+vancouver&tbm=isch
Yes going to Capilano and Grouse on Sunday is your best strategy. Need to double-check the start of the road closures, otherwise.... hit the shuttles before lunch to avoid problems. Another Grouse strategy is to use the Seabus and public transit to get out of downtown.