I don't know if this is the ONLY hotel Princess used, but they put us in Captain Cook hotel. We've stayed there in the pasted and enjoy the location, so we will be returning for an extended stay between cruises.
When I was searching for a rental car in Saint John, I came across Enterprise, along with Avis. I ended up booking with Avis, so I don't have any first hand knowledge of the Enterprise company. Enterprise is located at 10 Crown St., Saint John, NB, Canada. It looks to be about a 20 minute walk from port, but maybe they would deliver a car portside. Good luck.