Check out app/design/frontend/rwd/default/layout/page.xml, do a find for "footer" and you'll get right to the Footer blocks. The "Quick Links" are actually set under various spots in System > Configuration.
Here's what I'd suggest:
Make local.xml (in the same folder as page.xml above) if you haven't yet, and remove the "Quick Links" and "My Account" blocks if you don't plan to use them.
<?xml version="1.0"?>
<layout version="0.1.0">
<default>
<reference name="footer">
<remove name="footer_links"/>
<remove name="footer_links2"/>
</reference>
</default>
</layout>