The First Ecumenical Council was held at the imperial palace at Nicea. Gathering that many people together required big spaces and the church did not have buildings of any notable size of it’s own to worship in (still mostly house churches at the time of legal emancipation). The emperor paid for everything, including transportation and meals, and he sent out the invitations.
The Council of Trullo (quinisext) was at an imperial palace in the city of Constantinople.
I think it safe to assume that the Lateran Councils were held in the Lateran cathedral, however they might have done much of their work in the palace of the Lateran (once to home of the Plautii Laterani family, and the Papal residence for many centuries).
Vatican Council #1 was also held in the basilica, but most of the preparatory work and committee work was probably done in smaller rooms nearby.
I don’t know about Councils like Basle, Florence, etc. but they certainly needed a big church to all worship together in (which is one reason why Florence was chosen).
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