From Wikipedia:

Tombstone tourist (otherwise known as a "taphophile", "cemetery enthusiast" or "grave hunter" or "graver") describes an individual who travels to visit cemeteries for the enjoyment of looking at old and unusual stones or to find the graves of famous people. The term has been most notably used by author and biographer Scott Stanton as the title of his 2003 book and his former website [1] on the lives and gravesites of famous musicians. Tombstone tourists are usually more interested in the historical aspects of cemeteries or the historical relevance of its denizens.

Taphophilia is a passion for and enjoyment of cemeteries.[1] The singular term is a taphophile.

Taphophilia involves epitaphs, gravestone rubbing, photography, art, and history of (famous) deaths. An example of an individual's expression of taphophilia is the character Harold in the movie Harold and Maude (1971).

Taphophilia should not be confused with necrophilia, which is a sexual attraction to corpses.