I propose that during the last week of any presidency that the President (and Vice President) make prank calls. The first six days would consist of calling Americans all over the country and having some fun reconnecting to the people. The final day would consist of calling a foreign leader, chosen by the American people and have the call televised for some good lighthearted fun.
More Americans would probably vote for the foreign leader to prank than who voted in the actual election. This could be done online, with the standings being hidden until the call is completed. Foreign votes will also be accepted.