Most parking in Carmel is right on the street. Spaces are limited in time in most areas, but around the fringes of the business district and the neighboring residential areas there are places with no time limits.
There are two public parking lots (what you call "car parks"). One is at the north end of Sunset Center with the entrance on 7th Avenue at the corner of Mission Street. You can park as long as you want for a fee.
The other parking lot, called Vista Lobos (because it has a great view of Point Lobos) is at the Northeast corner of town (at 3rd and Junipero). There's no charge, but it's fairly remote. It's also at the top of a hill so you have to walk 4 blocks uphill from Ocean Avenue to get back to your car.
Edited: 6:38 pm, March 13, 2013