Using an up to date browser, like Firefox, Google Chrome, or Internet Explorer would allow you to stream from places like NPR or Stitcher and also allow you access to YouTube and also Spotify (Spotify has a web version of their app).

Having a high-speed internet connection would help, but listening to music or even listening to music on YouTube wouldn't require alot of bandwidth / a fast connection.

If you don't have a fast connection at home, you could visit someone you know who does have reliable access to the internet or go to a library and download the browser onto a USB ("thumb") drive and then take the browser home and install it on your home computer.