It depends, the Romans had two types of fora (plural of forum):
the forum civilium and the forum venalium. The former was the civic
centre, the latter was a commercial forum, or market. In the forum
civilium there would be the seats of the administrators, the
courts, the senate house (the municipium, local council, had a
senate with local competence modelled on that of Rome), the seat of
the local assembly of the tribes (if it was based in that town), an
area for public speeches, public buildings (basilicas), important
temples, shops and entertainment.
At the Forum Magnum (the Romans called it Forum or Forum Magnum,
Roman Forum is a modern term) in Rome there was also the the
aerarium (the treasury) the tabularium (the state archives) and the
regia, the residence of the pontifex maximus, the head of the Roman
state religion.