We stayed in Manarola and also had a rental car. We originally didn't want a rental car in CT but the logistics just worked out better with where we came from and where we heading to. They have a parking lot in Manarola that was wide open, but this was in October and we got there in the afternoon. It was $20 a day and there is a fellow in the parking lot who will transport bags for $6 each, but you need to arrange it through your hotel and contact him when you arrive. It was about a half mile walk to the hotel.
Many talk about using the trains from the parking lots but often that is quite a hike and getting on and off the crowded trains with luggage would have been challenging for us. We just parked the car and enjoyed using the train for the 2 days we were there.