Michelle, I infer from your question that you are unfamiliar with Vancouver. The western half of downtown Vancouver is one of the most densely populated places in North America. The eastern part is packed with commercial skyscrapers. During the Olympics, parking is going to be severely limited, street parking will be nearly impossible, and I won't be surprised to see lots charging $40 per day for cars.
The amazing thing is that the Capiliano park is so close to downtown. Surrey and Langley are farther out that the spots gbaglo mentioned, but are also worth a look. Be prepared to take transit buses downtown.
Do you have event tickets? For what events on what days?
And where are you located, btw?
Ron