I saw pictures of this meeting in the Oval Office in various magazines soon after it occurred. My memory, like so many of us here, isn't always perfect, but seeing this photograph brings it all back.
Elvis gave the President a gun and the President gave Elvis a badge. The badge is on display at Graceland and the gun is on display at the Nixon library. There was a book written in 1994 (actually more than one book recounts the meeting) and a movie about it in 1997.
You can also read a short article about President Nixon meeting Elvis.
*According to the Richard Nixon Library & Birthplace Foundation, the photograph of President Nixon's meeting with Elvis Presley in the Oval Office is the most requested image in the history of the U.S. Government.
Spoiler: Look closely or click the link under comments for help