If it's OK to block access for everyone who uses that computer, you can edit the HOSTS file to null-route non-approved websites, redirecting them to an IP address that doesn't exist (or, if you want to be annoying, redirect them all to something like nyan.cat).
As an admin, press Win+R and type
in the dialog box, and press ENTER. On the list of files in Explorer, right-click on "hosts", click "Open With" from the context menu, and then open it with Notepad. Once you're in, you can edit it like this:
#blah blah, more sites here
<paste the contents of http://pastebin.com/63hfPx8M here>
This null-routes all TLDs (.com, .net, etc.) and only allows through whitelisted sites.
To whitelist more sites, add a line for each website to the HOSTS file by putting the IP address of the website (see below), then a space, then the website name. Don't put "http://" in the name, or anything after the .com/.net/whatever TLD the website has.
To find the IP of a website, first do Win+R, then "cmd", then Enter. When the black box comes up, type
ping <website> and press Enter. (Again, don't put "http://" or any of that stuff in.) Some stuff will show up, but what matters is the IP, which is in brackets:
Pinging google.com [126.96.36.199] with 32 bytes of data:
So Google's IP is