You do not want, or need, a car in Vancouver. Finding parking is difficult and expensive. Public transit is terrific, and will get you everywhere you will likely want to go. Do be careful if you decide to book an Air b&b or VRBO, as others have mentioned, there has been a crack down on them, but there are still some illegal ones out there. Someone mentioned staying in the Kitsilano area. It is a nice area, but your options for transit would be limited to bus routes so I would check how close a place is to the bus routes, first. Also, if you are close to a train station, you can purchase a day pass from the ticket machines, but can’t purchase one on a bus. Some retailers do sell them, but you will have to find one near you. A day pass costs about $12, and is good on the bus, Skytrain, and Seabus, but if you purchase a ticket on a bus, you can’t use it on the train.
Hotels in Vancouver are expensive, and there is a shortage of them, especially when the cruise ships come in. If you don’t mind being a little out of town I would suggest looking at the Riverrock near the airport. It is directly connected to the Skytrain. It takes about half an hour to get into Vancouver from there, but you can also get off along the way to connect to a bus that will get you to other places. Another option might be to look for something in North Vancouver near the Seabus terminal. It only takes 15 minutes to ride the Seabus from Waterfront station (right beside Canada Place) across to Lonsdale Quay on the other side, and there is a nice public market there, and buses that will get you to Grouse Mountain and the Capilano suspension bridge, two very popular places for tourists.
Here is the link for transit https://www.translink.ca/