Rental car park for Cinque Terre at La Spezia train station

Since you are driving from Stresa I would park at Monterosso. It is closer to Vernazza (which has a very small lot with limited space), and coming from where you come, come before La Spezia.

There are two main parking lots in Monterosso. One is an open lot on the Fegina beach (the “new” part of town), one is a multistory parking structure (called Loreto parking) above the old town. The former is a short walk from the station.

But ask your accommodations about the possibility of parking in Vernazza, which has a small lot but maybe your accommodations can give you a parking permit (many stalls are for residents with permit only).

Fegina Parking near the station:
https://maps.app.goo.gl/qd43cJrXKPTXWeJ79?g_st=ic

Parcheggio Loreto (multistory) near the old historical center of the village (longer walk from the station)
https://maps.app.goo.gl/jjmWy8fDSVL5DtVK6?g_st=ic

From Monterosso to Vernazza is less than 5 min by train.

But if you insist on the farther La Spezia, this is the parking you want:
https://maps.app.goo.gl/zVM5hncaBCpxJjS7A?g_st=ic

The roads to Cinque Terre after La Spezia are curvy and sometimes narrow, and you can't use your car there anyway. The La Spezia Centrale parking is explained here: https://cinqueterreinsider.com/tag/parking-in-cinque-terre/

Since you are coming from the north you might also consider parking in Levanto. It's a somewhat shorter drive but much less urban. It uses the same Cinque Terre express train. https://www.cinqueterre.eu.com/en/parking-levanto

Very helpful responses, thank you everyone!