Nginx logging "_" instead of domain name
After reading the docs a second time I realized that the "_" is the referer.
I ended up going with:
log_format timed_combined '$remote_addr - $remote_user [$time_local] '
'"$request" $status $body_bytes_sent '
'"$http_referer" "$http_user_agent" "$host" $request_time';
Which appends the host and the time the request took to process to the end of the log.