was just there but only for 1 day - we actually drove in to Vernazza - needed to walk the last 1K down on road but as was not high season driving was not an issue. It will be when you are there.
You do not need a car to navigate the CT - there is a train that runs between the towns and there is also frequent ferry service. You can leave your car in the lots at the northernmost town (cannot recall name) and then if you want to explore the region you can hop the train to the car and then off you go.
Suggestions for day trips - take the A12 South to Carrerra - visit the marble quarries or go a bit further south to Forte de Marmi and visit the shops - good Wed market that has reputation for well priced cashmere sweaters - did not make it this trip but need a reason to return!
You will have no problem filling 3 days however in the CT - lots of hiking and even if you stick to only the train and ferry you should really enjoy being there. Not sure what the market schedule is for the various towns of CT but you should be able to find info on line someplace.
Enjoy