Banning you from the museum raises questions about your due process, equal protection, and First Amendment rights.

Generally speaking, a person banned like this would be unlikely to collect any damages, but may be able to obtain injunctive relief to prevent the museum from enforcing its ban. Of course, it would depend on the reason for the ban and the procedures the museum went through in imposing the ban and permitting you to challenge it.

In your case, though, the ban has already been lifted, so there's probably not much room for any kind of legal action.

**EDIT:** Since there are several people contesting -- with no law to support them -- the validity of this answer, here's a case discussing the First Amendment implications of access to museums:

 > As a limited public forum, there are certain First Amendment activities permitted on [National Civil War Museum] grounds and others that are not. For example, lectures or programs on a Civil War topic authorized by the museum and the public's attendance at these activities would be permitted uses, but activities concerning other topics (including the immorality of homosexual activity) would not. [*Diener v. Reed*, 232 F. Supp. 2d 362, 385 (M.D. Pa. 2002), aff'd, 77 F. App'x 601 (3d Cir. 2003)][1].


  [1]: https://law.justia.com/cases/federal/district-courts/FSupp2/232/362/2521147/