For some schools, anyone can go into the online course schedules to see the number of enrolled students (or the maximum) for any class of interest. Vasser has its “Ask Banner” listings:
https://aisapps.vassar.edu/cgi-bin/courses.cgi
For example, in Fall 2014, the largest history class had 30 students. Only about 1 in 5 had more than 20.
And keep in mind, almost every Vassar class will be taught by a professor who already has a PhD.
UCLA also offers public access to course listings. You have to link into each individual course to see the enrollments.
For example, the History 1A (Western CIv) lecture enrolled 227 students in Fall 2014.This course also has 50 min/week discussion sections (which presumably are led by grad students.) Those sections typically enroll 10-20 students.
http://www.registrar.ucla.edu/schedule/schedulehome.aspx