Follow these Steps:
1) Click on "My Account" on your Nike Plus Screen
2) Under "My Profile", please be sure to clear and delete any zip codes, country, states and click "save"
3) Click on "Site Preferences" and swap to metrics and you will be able to save now.
Alternate solution (if the above steps does not work for you) from Mr Anonymous from the comments:"To view your activities in km and km/h, just change the countrystettings at the bottom left of the nike+ site (just scroll down). Press English and then select English -> Europe. Automaticly your activities will be displayed in km. Don't try to change the site preferences, it doesn't work. I've been frustrated since 1,5 month and now I can finally see my activities in km, just by changing the countrysettings. Simple solution which Nike doesn't seem to know themselves!"
Solution as of June 2012
Alternate solution #2 (if the above steps does not work for you) from Gunnar Birk Kristiansen's comment:In order to change my Nike+ website from miles to kilometers, I had to put an extra digit into the ZIP code field to make it work. In my case I changed 2400 to 24000 - voila!
Solution as of August 2014