Car parking is of central importance to congestion on roads and the urban planning process of optimizing road networks, pricing parking lots and planning land use. The efficient placement, sizing and grid connection of charging stations for electric cars makes it even more important to know the spatio-temporal distribution of car parking densities on the scale of entire cities. Here, we generate car parking density maps using travel time measurements only. We formulate a Hidden Markov Model that contains non-linear functional relationships between the changing average travel times among the zones of a city and both the traffic activity and flow direction probabilities of cars. We then sample the traffic flow for 1,000 cars per city zone for each city from these probability distributions and normalize the resulting spatial parking distribution of cars in each time step. Our results cover the years 2015-2018 for 34 cities worldwide. We validate the model for Melbourne and reach about 90% accuracy for parking densities and over 93% for circadian rhythms of traffic activity.