It is going to be about a 2 hour drive south of the Interstate from either Livingston or Bozeman.
But remember the park is huge - that is the drive time to the entrance of the park. Once in the park it will be a couple more hours to get anyplace. Depending on traffic, time of year etc. I would say it would take about four hours (or longer) to get from I90 to Old Faithful (which is what most folks think of when they think of Yellowstone).