The coming of automated vehicles (AVs) and Mobility-on-Demand (MoD services) is expected to reduce urban parking demand and correspondingly alter the urban parking landscape in a significant way. Multiple modeling efforts have already demonstrated that Shared AVs (SAVs) have promising potential to decrease urban parking demand. However, previous studies have only examined SAV parking demand at one point in time, with various market penetrations. It remains unclear what the demand reduction trajectory will be like during the transition period when there is a mix of SAVs, Privately-Owned AVs (PAVs), Shared Conventional Vehicles (SCVs), and Conventional Private Vehicles (CPVs). This study fills this gap by developing an agent-based simulation model to examine the spatially and temporally explicit parking reduction trends with mixed travel modes from 2020–2040. The results indicate that in the most optimal AV and MoD adoption scenario, the parking demand will decrease by over 20% after 2030, especially in core urban areas. Meanwhile, the parking demand in residential zones may double, which could lead to transportation equity concerns. Additionally, parking relocation may also induce environmental issues by generating a considerable amount of empty Vehicle Miles Traveled (VMT). To reap the benefits brought by AVs and MoD systems and to mitigate the accompanying social and environmental issues, our results suggest that proactive policymakers in the next decade will need to modify land use regulations for both new developments and existing parking infrastructure in commercial and residential zones, as well as update travel demand management policies.