in CINQUE TERRE VILLAGES (East to West)
RIOMAGGIORE: There is a parking lot and also a parking structure at the entrance of town. Except for July and August I always found plenty of parking (although not cheap). Reaching Riomaggiore requires comfort driving in narrow spaces as the last mile of the road is a two way narrow lane.
MANAROLA: Parking here is really limited, mostly along the road. I wouldn't chance it.
CORNIGLIA: Same as Manarola.
VERNAZZA: There is a parking lot open to non resident about 500m before the entrance of the village. Not too many stalls though.
MONTEROSSO: Probably the most parking options among the 5 towns. There are two parking lots. One near the beach on the Fegina side (new town). Another at the Loreto side, at the entrance of the old historic village. Both are decent size. I never had problems finding parking here, even in July and August (but never went on a weekend on those months).
Outside CINQUE TERRE:
LEVANTO: It's the next village west of Monterosso. Plenty of parking lots near the beach and near the station.
LA SPEZIA: Huge parking structure at the station.
If it were me, I would look for accommodations in Monterosso (also most choices of accommodations). That way you are reasonably assured you can park in town. Monterosso is also easily accessible by car (from Levanto). Riomaggiore is another option too. Of course Levanto has the most, but it is not technically part of the 5 villages of Cinque Terre.
I wouldn't try to park in the other towns between Riomaggiore and Monterosso, because parking is really tough (at least before Covid, maybe now it's ok).