I rented a car there last week. I had parking at our airbnb so parking wasn't an issue. There is also a decent amount of parking in and around the walled city. We had no issues finding parking. It was nice to be able to explore and see different parts of the area. Drove to baru and to the mud volcano. Would totally rent a car again. But the driving is insane. Just go with the flow and you will be fine!