Where is Photostream data stored? I don't have to be connected to the internet to view them on my phone. Is it storing the current ones on my device?
They are stored on your iPhone. You can find them in the Photos app.
It's a smart album filled with photos taken in the last 30 days.

Comment by Jaberg: (thanks!)  


  The Photo Stream smart album on an iOS device will contain the 1000
  latest photos. The main "cloud store"will contain the photos from the
  last 30 days and those photos will all be viewable/downloadable from a
  computer.