Anything before 1828 and between 1864 and 1876 would be interesting to see how the game system would handle it. The problem with before 1828 is that the system with two parties, holding conventions and nominating a candidate, really only started with 1828. Treating the Federalists as a political party is anachronistic. The problem with the Civil War and reconstruction elections is that the Republicans were prepared to cheat to keep the Democrats out in all of them, and only relented after 1876 when it became too obvious.
Among more normal elections, the three following 1876 were all really close and pretty much forgotten, and could be interesting. I think 1856, 1940, 1980, and 2004 could be interesting campaigns. Really bad ones would be 1852, 1908, 1920, 1924, 1932, 1952, 1956, 1964, and 1996.