We have just returned from a week in Manarola. We drove into the area, but discovered that parking in or near the tiny villages is very difficult and expensive. The free parking spaces along the roads were all taken, and even the paid spaces were full when we arrived on a Saturday. Paid parking there costs 20 - 25 Euro/day. It may be possible to arrange for a parking space with the hotel or pension owners, but it will likely be expensive as well.
We left our car for the whole week in La Spezia in the Piazza d'Armi free parking lot. It was about a 10 minute walk from the La Spezia Centrale station. The train ride from La Spezia to any of the villages is short.