The place to park your car is the estacionamiento. It is the noun for a parking lot or a parking space. The verb is reflexive and is estacionarse.
One of the worst “spanglish” words I have heard is parquear meaning to park. I suppose out of all the bad combinations of English and Spanish I have heard, that is the one that bothers me the most. But, I do have to admit that parquear is much easier to say than estacionarse.
I read that estacionamiento en bateria means to park in a normal way where you put the front end or back end of your car into the parking spot. And parallel parking was referred to as estacionamiento en lÃnea. I don’t know that I have ever heard these terms used.