I see a lot of suggestions for free or open-source analytics packages, but I would refrain from recommending anything you haven't personally used. I've tried to separate myself from Google in various ways, and one of those was to replace Google Analytics with open source software. I tried several; they're all either non-functional out of the box, or require significant time investment to even start approaching Google…
If you're using AdSense, you're already giving Google your visitor data, no matter what visitor analytics package you use.
FTFY