Basic information is easy to grab from your server logs. Unless you're doing much more detailed stuff (journeys through the site, in-page interaction, etc) then you may not really need google analytics. You can probably do a lot more with just logs than I expect, but the most basic thing that a lot of people want (basically just a hit counter) is easy enough to get.

I've been having success playing with http://goaccess.io/ recently. Not doing much with it (partly as nobody is really visiting my site and there's not yet much real content up :)) but it seems good and doesn't require you to change what you're doing.