Not the easiest thing to find when you search on a search engine.
Though there is plenty places near by and even one on the outskirts of Ushuaia.
There is a few free/wild campsites (camping municipal) in the Tierra del Fuego National Park and near Rio Pipo. Problally the best looking one, from what I have heard is the one near Largo Roca. Though remember that you have to pay an entrance fee, $85(Arg), to enter the National Park, so not that free as campsite.
By talking to some other cycle tourers I leant about a campsite in the town, so much for the tourist information. Just west of Ushuaia is La Pista del Andino, up a rather steep hill, but then again if you managed to get this far it is nothing for your legs. :)
I did find the url (http://www.http://lapistadelandino.com.ar/) before but at last check the site was dead. But from what the cycle tourist, and that we stayed there two nights, it is still running.
Beautiful site, with views over the western part of the town, right at the bottom of the ski lift.
At time of writing it is $35(Arg) per person per night. Great showers, wifi and a bar. Our pitch was nicely hidden from the wind behind the trees. You even got a few horse and quite a few dogs walking around the site.
Some other campsite around Ushuaia:
http://www.campingriopipo.com.ar/ (around 12km west of Ushuaia)
http://www.haruwen.com.ar/ (around 36 east of Ushuaia)
More to come.