Classical/Jazz piece on player piano - what is it?
 

My dad was visiting a hospital the other day and they had this player piano that was playing a really pretty piece. He took a video of it so that I could hear it. My trouble is that it sounds familiar, yet I can't place it. I've played classical piano for over 20 years and am still having a hard time. I feel it could be Debussy or Gershwin, but there are so many easy-listening or smooth jazz pieces out there now that it's hard to identify. Here is the video:

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Thank you in advance to anyone who tries to help! :)