I saw it on GFY where someone was asking about a Google Analytics replacement and someone mentioned
Piwik. The first thing that goes through my mind when I think of replacing Google Analytics is that whatever solution I choose (if it's in house) is going to be a pain in the ass to set up!
Thankfully nothing could be further from the truth. Piwik took as long to set up, and was as hard to set up, as a Wordpress installation. In fact, the information requested is basically the same. You might have to run some SSH commands or use FTP to change file/directory permissions, but that is it.
Part of the install is spent setting up your first site. So once done you get to see some immediate stats. Keep in mind that your first site is going to be the site/URL from which all of your other sites will load the analytics script! So plan to use a mainstream name and/or one you will be keeping for a long time.
Anyway... If you are looking to use something that has instant stats and keeps your data private, Piwik is a very easy solution!