There is controlled parking immediately outside the apartment in Chandos Square and Victoria Parade. It operates every day even Sundays and Bank holidays. Sometimes also until 10pm so please check carefully. That said, the apartment is so central that you don’t need to use your car if you are remaining in Broadstairs.
Please see this link to Thanet District Council’s parking page for information about where to park: http://thanet.gov.uk/yourservices/parking/
There is unrestricted on-street parking in roads approximately 5-10 minutes away, all the roads to the south starting with Granville Road. We often drop our stuff at the apartment and then park on the Western Esplanade overlooking the sea (or any of the roads running off it such as Seapoint Road, Palmerston Avenue, Dumpton Park Drive, West Cliff Avenue) and then take a lovely walk back to the apartment along the promenade over Louisa Bay and past the Bandstand.
Note that parking right outside the property in the Chandos Square is almost twice as expensive as parking along the seafront ie Victoria Parade which is 10 feet away (crazy but true).