The earliest public structures were places of assembly known as moot hills. These were generally simple earthen hills and occasionally they incorporated earlier prehistoric burial mounds. Such a mound, known as the Doomster Hill, stood in Govan until the 19th century. It was built on a colossal scale (forty-five metres in diameter and five metres high) and had a broad step halfway up and a flat top. Its size and location suggest that the British kings of Strathclyde used it in the 10th and 11th centuries. A smaller court hill known as Gallow Knowe with the same distinctive stepped profile survives in Rutherglen.
The Cathedral also served as public space. The nave was given over to the laity who erected altars there and used it as a place of business. As the largest covered space in the burgh it may have been informally used for public assemblies. Legal business was certainly conducted in the Cathedral because the Bishop enjoyed judicial superiority over the burgh. The Bishop's court met in the Consistory House in the south-west cathedral tower.
A tolbooth was provided for the municipal administration of the burgh from at least 1454. The main responsibilities of the baillies related to the regulation of the market and the collecting of tolls and fines. Nothing is known of the appearance of the building and it can only be supposed that it stood on the site of the later Town House. The ground floor of this building was let out to merchants, while the upper floor presumably contained a hall for meeting and the conduct of business and may have housed a jail.
The origins of the Grammar School are unknown, but it was a practical requirement for a cathedral to have a school so it may well have been organised in the 12th century. The University (established 1451) was originally located in Rottenrow, but little is known of its buildings prior to the Old College.