This paper seeks to systematically explore the efficiency of the uncoordinated information-assisted parking search in urban environments with two types of parking resource facilities: inexpensive but limited facilities (public) and expensive yet unlimited ones (private); an additional cruising cost is incurred when deciding for a public facility but failing to actually utilize one. Drivers decide whether to go for the public or directly for the private facilities, assuming perfect knowledge of prices and costs, total parking capacities and demand; the latter information can be broadcast by an ideal centralized information dissemination mechanism, assisting the otherwise uncoordinated parking search process. Drivers are viewed as strategic decision-makers that aim at minimizing the cost of the acquired parking spot. We formulate the resulting game as an instance of resource selection games and derive its Nash equilibria and their dependence on the environmental parameters such as the parking demand and supply as well as the pricing policy. The cost at the equilibrium states is compared to that under the optimal resource assignment (dictated to the drivers directly by an ideal centralized scheme) and conditions are derived for minimizing the related price of anarchy. Finally, the numerical results and the presented discussion provide hints for the practical management and pricing of public and private parking resources.