The best replacement for google music is itunes.

The best alternatives to google music are rated as following:
★★★★★  itunes
★★★★★  spotify
★★  rhapsody
★★  xbox music
★★  beats music
★★  amazon cloud
★  itunes match
★  amazon cloud player
★  amazon mp3
★  doubletwist
★  sony music unlimited
  poweramp
  deezer
  amazon music

Your alternative for google music is not listed? Suggest!
Speaking about google music, one probably shouldn't forget about poweramp.

Other search terms related to google music and their ratings are:
★★★★★ poweramp
You have in mind a companion for google music and it is not yet here? Propose!



Google Trends

Scale is based on the average worldwide traffic of google music in all years. Click on graph for more.
google music
itunes
spotify