After a super easy installation (just a component and a mambot) it directly started to collect the stats. These are presented verry nicely on the admin page.

All stats applications will provide you with visitors IP addresses, maybe even nslookup info. JoomlaStats (starting from version 2.1) now even provides (Joomla) logged in user information!

There is even a (beta) module available to show top visitors (by Joomla username!) as number of visits and/or number of page hits. Another (beta) module shows you the latest visitors.

Just give it a try...