Where to stay in Cinque Terre-we have a car and 4 people

You can stay at any of the villages, as long as you are aware that you may not be able to drive right up to your accommodations as those villages have traffic restrictions and are largely pedestrianized.
Monterosso and Riomaggiore have parking facilities just outside the old core (which is closed to traffic), so you could park at those lots for the length of your stay (prices should be around 20-25€ a day). The other villages have minimal parking availability, and often restricted to residents only, so maybe not ideal for visitors with cars.
Roads to the villages are narrow curvy roads, so pay attention not to scrape the walls.
There might be instances where two vehicles going to the opposite directions may not be able to easily pass due to the narrow streets. The rule of the road in Europe, in that case, is: the vehicle going downhill must yield to the vehicle going uphill and park as close as possible to the right so as to permit the upcoming vehicle to go through.

RIOMAGGIORE:
Riomaggiore Park (multistory). You can see the top story on the satellite photo of Google Maps. I often parked here.
https://maps.app.goo.gl/BSQeWoNArge8BSfe7

MONTEROSSO (OLD TOWN):
Loreto Parking (multistory):
https://maps.app.goo.gl/Fu68e7WKcDz75yRV8

MONTEROSSO (FEGINA/NEW TOWN)
Fegina Parking (open air pay lot). I parked here once or twice decades ago, when living in Italy.
https://maps.app.goo.gl/VfZMojYVCvH6QjvC9

There are also spots available for parking in the streets (maybe), however if the stalls are marked by BLUE stripes, it means pay parking (find a meter machine to get a ticket to place on dashboard). If the stalls are marked by YELLOW stripes, don't park there, as they are reserved for someone (to residents, to handicapped, to official vehicles)

As I said the other towns have minimal parking facilities. If you go there, make sure you park in the blue striped stalls (pay parking), not the yellow striped stalls:
MANAROLA
Posella Parking:
https://maps.app.goo.gl/agg4wymW3tdvbv52A

VERNAZZA (VERNASSOLA)
Vernassola Parking lot. The small one that was near the village is now for residents only. So for visitors only the two small pay lots below at Vernassola are available. It's up the hill, and kind of a walk to the village down below.
https://maps.app.goo.gl/DT1tBCiHYYyj7RPn7
https://maps.app.goo.gl/L8ewK2b2fqH1cX2YA

We stayed in Monterosso at Hotel Porto Roca which has beautiful sea views. Monterosso is the largest of the Cinque Terre villages and offers more dining and parking options too. Highly recommend Monterosso.

Take a look at Affittacamere PZ in Vernazza. It's up in the hills overlooking the town, and you get FREE parking. The rooms are reasonable, simple and clean. The main thing is the amazing views over the hills. We sat outside at dusk each night, and could hear church bells and far away laughter. There is a pretty path past vineyards and the old church down to the town, where you can walk to the other villages, take the train or catch the ferry. There is also a shuttle bus (my choice for coming up to the hotel.)

We stayed in Manarola at Hotel Marina Piccola, and we thoroughly enjoyed our stay here. We did not have a rental car so I can't help you with that. However, in addition to the other parking places mentioned here, I believe you can park your car in a garage in La Spezia, and then take the train to the village you are staying in. I personally believe that staying in one of the villages is nicer than staying in La Spezia. And you are wise to spend 3 nights in CT. That's what we did, and it was much less crowded before 10AM and after 4PM. The evenings were lovely, and the sunsets were stunning!

Thank you all! Great suggestions, I will see what might be available.

Our Rick Steves tour stayed in Levanto, just north of the Cinque Terre villages, which I enjoyed a lot. It was a quick train ride to the villages. You might want to check that location out. I’m guessing that driving and parking would be easier there.