Cinque Terra with a car...ideas please.

Look for a place to stay in Monterosso. They have a parking lot at the beach and some hotels in the Fegina area (new area of town) even may have some parking. Then once you park the car for your stay, just rely on the trains to take you to the other towns. The Monterosso station is between the old town and Fegina. When you drive to Monterosso take the freeway to Levanto, then in Levanto follow the directions to Cinque Terre. Follow directions to Fegina.

Some hikes are more challenging than others. The easiest is from Riomaggiore to Manarola. Also Manarola to Corniglia is doable. If you don't care to hike at all, just use the trains and maybe the boats. I haven't done the hikes for a very long time, but I still enjoy going sometimes (mostly to take people who have never been) and I always drive from Florence just for the day. There is a car park also in Riomaggiore, but not that big. Also not cheap. Getting to Riomaggiore is also a bit more challenging than Fegina (narrow road). Another alternative is to stay in Levanto, which is not part of the 5 terre, but it's the next town after Monterosso, so very near by train. Levanto is also easy with a car. Parking in all other towns is really limited, so don't bother.
I don't have hotel recommendations to make in Monterosso (or Levanto), but other here might. Or just try to search on a search engine.

The Rick Steves Italy book contains a lot of recommendations for places to stay in the CT for all budgets. He also talks about the transportation options.