Upvote:2
It depends on where you're staying and how close is 'near' to downtown. However, this website - Parkopedia, shows you where the parking places are in Vancouver, and some are either free or $1/hour, and several are available 24 hours a day.
Upvote:3
If you are staying in a hotel, you might want to get in touch with them and see if they have parking and how secure it is. Many hotels have their own lots, and if they are only available to guests, then you would assume that they are more secure than your average city parking.
Even if your hotel doesn't have its own parking, they can probably recommend a location which is close by and meets your requirements.