iPod Nano without iTunes (Chromebook) My father has an iPod Nano (4th generation I think, though it may be 5th) and runs iTunes on his aging Windows laptop.  He would like to switch to a Chromebook, which would obviously prevent him from running iTunes locally.

Are there alternative (cloud-based) ways of syncing music to an older Nano device, or is a PC with iTunes required to store music and sync this device?
Simple answer: No.

iTunes and a USB cable are needed to synch any iPad Nano. The 7th generation Nano has Bluetooth, but that is for playback only. This Wikipedia page on all the generations of Nanos will be elucidating.