Which level of scrutiny is applied to content-neutral restrictions?

Hypo 1: The city of Hypovale bans all signs and posters on public property in order to keep things looking neat and tidy. Sam wants to put up flyers protesting the mayor's policies, but the city tears them down, citing the signage ban. Result: The city's rule against signs is content-neutral, since it applies to all signs regardless of what they say. As long as Hypovale can show that it has an important interest in avoiding visual clutter, and that banning signs altogether is a reasonably targeted way to achieve that goal, the restriction would likely survive intermediate scrutiny. Sam's political speech doesn't get special protection here. The First Amendment doesn't guarantee him the right to post his message anywhere he wants.

Hypo 2: New Hypoland enacts a law requiring a permit for any gathering of more than 25 people in a public park. The application process takes 30 days and costs $100. Bob wants to hold a rally next week to protest police brutality, but he can't get a permit in time or afford the fee. Result: The permit requirement doesn't seem to be motivated by the content of anyone's speech. But it seriously burdens political demonstrations and other expressive gatherings by making them harder to organize, especially on short notice. A court would likely find that it restricts substantially more speech than necessary and fails intermediate scrutiny. The government's interest in regulating large crowds could be served by a less complex permit process.

Hypo 3: Hypofornia bans targeted picketing within 500 feet of any residence. Bob wants to lead a protest march through a neighborhood where a politician he opposes lives. The police order him to stay 500 feet away from the politician's house. Result: The law is content-neutral because it doesn't target any particular message or point of view. Its purpose is to protect the privacy and tranquility of people's homes. A court would probably decide that this is a significant government interest, and that a 500-foot buffer zone doesn't burden more speech than needed to serve that interest. Bob is free to picket elsewhere, just not right in front of someone's private residence.

Hypo 4: At the Hypofornia State Fair, there's a rule that says demonstrators can only gather in a certain designated area and can't approach people to hand them leaflets or petitions. Bob tries to collect signatures for his petition protesting animal cruelty, but he's told to stop talking to people and go to the "free speech zone." Result: The restriction on petitioning at the fair is content-neutral, but it might not pass intermediate scrutiny. The fair probably has a legitimate interest in maintaining the orderly flow of foot traffic. However, a court could find that relegating all demonstrators to a limited area unreasonably confines speech to an out-of-the-way "ghetto," rather than narrowly serving the state's crowd control needs. Letting people share their views more widely while leaving room for others to pass by might be a better balance.