The City of Ithaca website states:
Odd/Even parking regulations are in effect from November 1st through April 1st of each year. Odd/even parking now dictates that from 7 p.m. on an odd-numbered calendar day to 6 a.m. the next day, cars must park on the odd side of the street. On an even day from 7 p.m. to the next day at 6 a.m., cars must park on the even side of the street. The hours were recently amended from the previous enforcement time, which began at 2 a.m.
This was recently updated to be more straightforward than it was historically. The new rule of thumb (when you are parking before midnight): park on the odd side of the street on odd days, and the even side on even days.
However, if you are parking after midnight things get a little more complicated:
In any case: when in doubt, stop on by whichsidetopark.info and have a computer figure it out for you!