My family of 5 need a place to stay for one night for my nephews graduation. hotels all sold out. any suggestions?

Is this Cornell or Ithaca college graduation?
You may have to try Syracuse and or Binghampton if are sold out. My experience was that you need to reserve a year in advance and for two nights, Not enough hotel rooms in town for the big graduation ceremonies.

You could try Binghamton, about an hour south of Ithaca. I think it's closer than Syracuse. There are also hotels in Auburn and Skaneateles, both of which are a bit closer than Syracuse. But if you are willing to drive an hour, you'll find something. I'm not good on the geography of the Finger Lakes region, but there may be other places closer by.

Watkins Glen is a half hour from Ithaca... google for hotels in all price ranges...

Watkins Glen and particularly Skaneateles are interesting and/or attractive places, worth a visit on their own. And I agree on two night minimums being likely, so being somewhere interesting is nice.

Cortland is closer than either Syracuse or Binghampton (which are almost equidistant in opposite directions).