This is a fairly weak reason, but if you want to stand on the marker where the four corners meet, you can have your picture taken standing in four states at the same time. You can take US 160 east from US 191, or US 64 west from US 491 at Shiprock, NM. About 35 miles from either 191 or 64.
I did it for an even weaker reason. Tony Hillerman was a novelist that set his Native American mystery stories in the area around Shiprock and a Navajo Policeman named Jim Chee. Alas, Mr. Hillerman passed away in 2008, so no more brain candy for me.