Though they never actually had a beer together, but Alex Koppelman over at Salon Magazine lists the Nixon-Elvis Oval Office encounter as among the top casual White House meetings:
On December 21, 1970, Elvis Presley got his wish and had a meeting with President Richard Nixon at the White House. He wanted Nixon to make him a "Federal Agent-at-Large" in the Bureau of Narcotics and Dangerous Drugs. According to notes taken by a Nixon aide during the meeting, Presley repeatedly told Nixon of his support for the president, and showed Nixon his wide array of law enforcement memorabilia, including numerous police badges from around the country. He even mentioned to Nixon that he thought the Beatles promoted an anti-American spirit.