Your best bet is to set up a local copy of MediaWiki. This is the same software that runs Wikipedia, but it's also the application that powers the Codex.
After you've got that installed, you can tell the Codex to export the pages you want and you can import the XML docs into your local installation. It's not automated, but it should give you enough information to work with for quick references.
All of the documentation for downloading, installing, and configuring MediaWiki is available online.
If you can run WordPress locally, you should be able to run MediaWiki locally as well (you need both PHP and MySQL to set things up).
Export the Codex
Make a list of the pages you want to export. I'd love if there were an automated tool to export everything, but in the absence of that let's stick with the manual process.
Navigate to http://codex.wordpress.org/Special:Export. This page lets you mark which pages and categories you want to export.
Lets say you just want to export the
Function Reference page. You'd enter "Function_Reference" in the large box for page names. Place one page name per line to export multiple pages at once.
But since that one page isn't very useful ... export the entire
Functions category instead. Enter "Functions" in the category box and click add. The Codex will automatically list all 964 function pages for you. Then just add a line for "Function_Reference" so you get the index as well.
You can see a list of all available pages at http://codex.wordpress.org/Special:AllPages. The list is quite extensive, so I won't cover it here ... but add every page you want exported anc click away.
Once you've clicked "Export," the Codex will generate a (rather large) XML file containing all of the content.
Import the Codex
Now navigate back to your local MediaWiki installation. You can now import the XML doc and create your local "clone" of the WordPress Codex.
Detailed import instructions are available on MediaWiki's website.