The incident is one of two which took place between May 7 and May 9, 2021.
The Makery at number 98 on the High Street was “kicked and damaged” at around 10.20pm on Friday, May 7.
Police have said they have now identified the person involved but they are still working to find the person responsible for the second incident.
The Central Cafe at number six West Port was targeted sometime between 11.30pm on Saturday, May 8, and 7am on Sunday, May 9.
The vandal threw what police described as “large boulders” against the window, smashing the glass.
Officers are still appealing for information to help them identify who damaged the Central Cafe.
If you witnessed anything, or have any information, you should contact Police Scotland on 101 quoting incident reference 0938 of 09/05/2021.