[1L]

But the school is in charge of administering it. For example, they can set hours of use.

Correct, but that is a TIME restriction, and not a content restriction.

[Diddle E. Squat]

But if a city can impose a 'use' restriction(no sleeping on benches in public, no dumpster diving), then it seems that some forms of activity can be banned. Could revolve around the issue of expression, though. However we are still talking about institutional property. If the school can't restrict use(such as the appropriate place and form of protest), then how is a judge allowed to restrict expression in his court room? Seeing as how UH provided alternative venues, then it seems that they are not blocking free speech, but redirecting it to appropriate locations.