Should I go to Osaka the night before from Kyoto for my flight?

I have a 2:50 PM flight from ITM to the US, should I book a hotel near Osaka the night before or is it fine to travel the morning of to ITM from the Higashiyama area?

If yes, is there a cheap hotel that is recommended? Is there anything to do near the airport on that last day?

Edit: My flight from ITM goes to NRT then onwards to the United States.