Your goal, is to wank the Wilson presidency as much as possible. Ideas...
-Earlier entry into WWI
-A milder Treaty of Versailles, WWII prevented; OR getting to the other extreme, have a harsher Treaty of Versailles, Wilhelm II convicted in Nuremberg-style trial and executed by firing squad.

-Get the US to join League of Nations
-A more effective League of Nations
-No stroke during his second term, survived beyond 1924
- A third term in 1920
- 4th term in 1924, or even a 5th term in 1928

- 1929 wall street crash managed better or prevented; no Depression or only a short recession
or, having him altering the system fundamentally :
-As an academician he seemed to favoured parliamentary system for the US. Get him to change the presidential system in the US to a more parliamentarian one like in the UK
Happy wanking!