In my opinion there are no longer any really viable server side analytics/log processing that's equivalent to what you get with GA unless you want to either install some kind of server with a ton of features and dependencies or use a tool that will most likely also require the use of js.
The amount of crawlers, botnet spam, hacking or scanning activity and other non-visitor related hits you get these days will require a lot of filtering, updating spamlists, blacklisting, etc and you'll probably end up spending more time tweaking your webserver and analytics setup than actually gathering any relevant information from said analytics.
That said, the "old" log processing tools like AWStats, Analog, Webalizer, etc are still available although I'm not sure if they've been kept updated. I'm sure there is also a lot of more competition on self hosted tools that try to replicate what GA does but I'm not that familiar with any either.
You mean to say that spambots don't respect robots.txt??
Good to think about. I'll check these out and see what they've done (if much) to mitigate that issue. I'd imagine that would need to be front and center, unless they're focused more on internal services.
Running nginx here