This place of national trauma was officially ignored for decades, as Dallas was uncertain what do to with its unwanted tourist attraction (though at least one of us recalls a family vacation there in 1967, staring up at the sixth floor, then at the road, then the grassy knoll, then the sixth floor...).
In 1993 it was declared a National Historic District, so nothing can be changed. This, combined with the city's original let's-ignore-this attitude, has kept Dealey Plaza almost exactly as it was in 1963 -- instantly recognizable to all conspiracy buffs and aging New Frontiersmen and women. You can sprawl on the grassy knoll (and keep an eye out for overlooked cartridge casings) or try to spot the small "x"s painted on the Elm Street pavement, marking the spots where bullets hit the President (They were paved over just before the 50th anniversary of the assassination in 2013, but someone will certainly paint them again). We do not advise running into the middle of this busy roadway for a picture, although people do.
Dealey Plaza has lots of little monuments that are mistaken as memorials to JFK, but that were in fact erected to Dallas citizens long before the events of November 22, 1963. We did see a 1980 Texas historical marker that pointedly notes that "Lee Harvey Oswald allegedly shot President John F. Kennedy." Helpful tourists have repeatedly carved an underline under the "allegedly." Another plaque shows the route taken by the Kennedy motorcade on a bronze map, and the X that marks the assassination spot has been worn shiny by countless tracing fingers (JFK's motorcade was allowed to drive the wrong way on one-way Houston St. -- thus one of the President's last acts was to place himself above the law).
When we were visiting, we also saw enterprising vendors hawking fake newspapers on the Plaza -- reproductions of the Dallas evening papers from 11/22/63, with screaming headlines announcing the assassination.