I think this is as good a place as any to point out that the Bill of Rights was written BY the government to set limits on itself for the protection of democracy. None of these rights are going to be open ended. The people guaranteeing you all these rights are the same people charged with the job of keeping you, and everyone else, safe. Be reasonable!
In terms of the right to assemble, there is going to be the requirement for a permit. Unless your demonstration is going to be invisible, in which case why bother? There are going to be traffic control issues, pedestrian safety issues, demonstrator safety issues, potential private property encroachments, and more. Courts generally bend over to make the life of the demonstrator workable. They are willing to ask the local authorities to be able to respond to a permit request in a matter of days. But not hours. The authorities have to adjust staffing because of you. The local authorities are allowed to set reasonable time, place, and manner limitations on your event. What they are NOT allowed to do is to have requirements that are too vague for you to understand, or requirements that leave too much discretion in the hands of staff. Finally, law in general embraces a concept of exhausting your remedies. What this means is that the ordinance which will allow you to proceed, or not, often has in it a clause that says something like, "If the police chief denies a permit, the applicant can appeal to the ?". If you ignore that information, and go right to the court house to sue, you may have the court simply bounce your petition back with the comment of exhausting remedies.
Bottom line, if you want to be a demonstrator, first do your homework, and second, be courteous. Good luck!