Alice stands in a public square holding a television that shows pornographic video content. Is she protected by the first amendment?
If the pornography is not obscene (see Miller v. California, 413 U.S. 15 (1973)), it receives First Amendment protection. However, First Amendment protection does not preclude restrictions (including criminal prohibitions) that are narrowly tailored to serve a compelling governmental interest (this analysis is known as "strict scrutiny").
Note that Ginsberg v. New York, 390 U.S. 629 (1968), which upheld a prohibition on the sale to minors of material defined to be "obscene on the basis of its appeal to them whether or not it would be obscene to adults," did so on a rational basis standard, in an area for which the Court would now apply strict scrutiny. The Court found that the state has an interest in the well-being of its children, and to see that they are "safeguarded from abuses." It found that it "was not irrational for the legislature to find that exposure to material condemned by the statute is harmful to minors." This reasoning has been described as an outlier and not consistent with today's test (John A. Humbach, "Teens, Porn and Videogames: Time to Rethink Ginsberg?" (2010)).
Whether that would be seen today as not falling within the protection of the First Amendment (attracting only rational basis review) or whether it would subject to strict scrutiny, the main point is that even for content that falls within First Amendment protection, there may be restrictions on that communicating that content. Your question and title, taken together, seem to assume that if the communication is protected by the First Amendment, it is necessarily permissible to communicate it in a public place; that isn't true.