I turned off all my auto sync and I restricted background data, thank goodness I have Wifi at home and work otherwise I'd be at 2/3GB of my limit in 1 WEEK.
Could syncing really use 2 GB of data in 6 days ?! That doesn't seem reasonable. This is a brand new phone I installed absolutely NO apps
What accounts did you link to your phone? Gmail? Dropbox? Drive? Do you have Picassa albums and are syncing those? Google+ user with auto photo upload?
There is plenty that comes preloaded that COULD give you a lot of sync time. Much of it does not work except on wifi however, so perhaps your worries about your data consumption are not as bad as you think. Maybe they are, just saying don't panic until you know what is up
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Do you stream music? Most streaming music does high quality when on wifi.
When you configured your phone, you probably linked a Gmail account. What are you syncing within that account? Look at the settings and see if any have a little ! next to it indicating a problem.
If you are shooting pics and have dropbox photo upload going (wifi only), I could get that usage with all the snaps I take some days.