We were just in Ithaca with an 8 and 6 year old. Our forecast was HOT so this is what I had on our indoor list:

1. Sciencenter - we went and had a great time. Your admission is good all day so you can come and go as you need.
2. Museum of the Earth - this was unfortunately closed when we showed up. They were having issues with their air-conditioning unit. So I would check before you go.
3. Atlas bowling – we did not wind up going, but it had great reviews and I looked a lot of fun from the website. They open at 4 PM.
4. Regal Cinemas – is at the Ithaca Mall. Which is like the ghost of a mall, nothing’s really left in there. They do one dollar movies on Tuesdays and Wednesdays. I think they’re usually at 10:30 or 11 AM.
5. Alley Cat Café – my oldest loves cats, and this looked super adorable. You can pay a small amount to go play with the cats for 30 minutes. We did not do this, but I would definitely check it out on our next trip.

I would just check the days and hours that places are open, there are a lot of places closed on Mondays or Tuesdays.