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 updated in 2019 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:

1. Most early mornings, you must park on the odd side on even days, and on the even side on odd days (since the relevant enforcement period started the day before).
2. On the morning of the 1^st day of a month following a 31- or 29-day month, the previous day is still odd and therefore you must park on the odd side.

In any case: when in doubt, stop on by whichsidetopark.info and have a computer figure it out for you!