You will need a performance analysis tool. There are several to chose from.
http://piwik.org/ is likely the best or near the best. Piwik is not a log analysis tool and uses a bug, but since it installed on your computer, it will be a lot faster.
Other options are:
http://www.awstats.org/ (log file based)
http://www.webalizer.org/ I have used this in past for my web host customers. (log file based)
I also used SawMill (still do) and created automated custom e-mail reports for my customers, but SawMill is fairly expensive.
I am not a huge fan of Google Analytics. There is valuable information that only Google can provide so it should be a tool in your arsenal. I do use it. But it does not give a complete picture of what is going on. Always use a separate log file analysis tool. Google Analytics can be confusing. However, a log analysis tool cannot provide what Google can so it remains a valuable tool. Both will empower you to make solid decisions.