Street parking is the closest but sometimes difficult to find. Turnover of spots is high so try waiting in one place for someone to leave.
Multistorey parking can be found at:
The Clift condominium. Entrance from Telok Ayer St.
Frasers Tower, 231 Telok Ayer St
The Ministry of National Development building (entrance from Maxwell Rd). Exit the carpark at the Amoy Street Food Centre.