I have gone on a couple myself, and I recommend doing the following:
1. As a general rule, don't participate and don't speak unless spoken to. It has been mentioned here, and I did just that for my visits. Exceptions apply from time to time, but don't speak in a class that others spent $3,000 or more to take, not to mention that they spend $20 to $30K in tuition that semester too for the class you are visiting for free.
2. Don't focus too much on the professor. Look at the students. After all, if you go to a particular place, the student quality should be around the quality of students you'll be with next year. How do they interact with each other? How do they respond to the class material and how is their input? In one of the visits I went to, the professor put students into random groups and put them in the breakout rooms. I got to see most of the student dynamic here, seeing guys take the lead, and throw their diverse ideas into the fire. That was a bit different than seeing the student go into their "comfort groups" which I didn't see, but I was impressed with what I saw in the random groups.
3. Feel free to ask the other students who aren't your host like his or her buddies. They may give insight on the interview process, school culture after hours, etc.
4. Get a feel of the general university campus too, aside from the b-school, if the b-school is on the main campus. If you like that schools city location, the other activities on campus, etc., I think you'll like that business school.