There have been many BatMobile, but none as beautiful or as worthy of the name.
The 1966 BatMobile, created for the TV series by the recently departed George Barris, is lovingly documented in this video.
I remember seeing the awesome BatMobile around Los Angeles as a kid in the 70s and 80s. Some dudes were taking it to early versions of Comicon and letting folks pose near it, and it was 'around.'
You can also take a hike to the Bronson Caves, and see the entrance/exit to the series Bat Cave, but the super cool car will not be there.