Some right to record in public may be protected by the current jurisprudence invoking the first amendment, but the first amendment itself obviously doesn't say anything about the right to record in public:

> Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances.