I second Google Analytics for getting a snapshot on the activity on your site. As far as FREE goes, it's the best out there.
For keyword research, Wordtracker and Keyword Discovery are both great. There are some free tools out there with limited capabilities. Do a google search for 'FREE SEO tools' and you will find some apps. There's also the outdated Overture Keyword Suggestion tool to get some data from...
Best of luck!
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