You could say
There are three institutions in this campus
However as Mark said in his answer, that would typically not be taken to mean three buildings. Rather, that would imply that three different universities all shared the same campus, or possibly that the university had three different departments. Or, it could mean that the university has a hospital and a church on campus, for example. It refers to organizations or groups rather than to *physical buildings.
Merriam Webster defines an Institution in this case as:
an established organization or corporation (as a bank or university) especially of a public character
For a better understanding, see the word institute, which wikipedia defines as:
An institute is a permanent organizational body created for a certain purpose. Often it is a research organization (research institution) created to do research on specific topics. An institute can also be a professional body.
In some countries institutes can be part of a university or other institution of higher education, either as a group of departments or an autonomous educational institution without a classic full university status such as a University Institute.
A "Facility" could be a building, but does not have to be. It could be a part of a building, or, it might not even be a building at all. Some other kinds of structures could be called facilities (water facilities, electrical facilities).
If you're really looking to describe buildings, try one of the following:
I got these from a thesaurus... I have to say that none really feel as right as "building" when talking about, well, buildings. :-)