Are you familiar enough with any to make a recommendation? If there's a good Wordpress plugin that will replace GA I wouldn't mind trying it out.
Back when I thought I could be the next blog-o-sphere sensation, I used Piwik with WordPress. It worked very nicely. It’s been too long for me to remember exactly which WordPress plugin I used for Piwik integration, but I think it might have been this:
http://wordpress.org/plugins/wp-piwik/
Depending on what your setup is, it may take a little elbow grease to roll your own Piwik installation. It was dead simple for me at the time because my Web host included a feature called Softaculous that did one-click installs of many popular programs including WordPress and Piwik.