I remarked at the time that I found the experience remarkably similar to buying a house. We looked at nicer houses than the one we bought (and that you visited) but they didn't quite feel right.
It might be difficult to precisely place your finger on what the 'thing' is that makes you think...
In both cases it was how we felt about the school when visiting ourselves. This meant that "better" schools, as assessed by OFSTED, were not our first choice.
So, I voted "Atmosphere you experienced during visits".