Tierra del Fuego
Tierra del Fuego (/tiːˈɛərə dɛl ˈfweɪɡoʊ/, Spanish: [ˈtjera ðel ˈfweɣo]; Spanish for "Fireland" or "Land of Fire") is an archipelago off the southernmost tip of the South American mainland, across the Strait of Magellan. The archipelago consists of a main island Isla Grande de Tierra del Fuego divided between Chile and Argentina with an area of 48,100 km2 (18,572 sq mi), and a group of many islands including Cape Horn and Diego Ramírez Islands.
Ferries to Isla Grande leave from Punta Arenas or Punta Delgada. Punta Delgada is much quicker to reach from the north, just a couple of hours over the Chilean border. The Punta Delgada route only takes 20 mins compared to a couple of hours from Punta Arenas, and also runs much more regularly, pretty much constantly to-ing and fro-ing throughout the day. There is much more regular traffic on this route. However Punta Delgada is just a ferry ramp and some workers in flourescent jackets whereas Punta Arenas is a sizeable town with things to do, so you may prefer the more scenic route with more to explore.
On the Punta Delgada ferry the car costs a set amount regardless of passengers, so you can explain to prospective lifts you needn't cost them any money or if needed you can offer to chip in. As far as we could tell there is no foot passenger option, but we had a ride so didn't bother asking, perhaps there is. Usually there is a queue of waiting cars so if someone has to leave you at the ferry you can probably find someone to take you on pretty easily. It runs all year round but depending on storms may always be held up for varying periods of time.
Once on Isla Grande there is another few hours of mostly gravel roads, all pretty windswept and barren, before you cross the border back into Argentina. Telling the customs you are hitch hiking is perfectly acceptable, and the border is as good a place as any to loiter for lifts (if a trucker can't pass through with you or something) as it provides a modicum of shelter from the wind. However be aware the Chilean and Argentine posts are twelve miles apart.
The Argentinenian-Chilean border (the one closer to Argentina) at Paso San Sebastián has a waiting room (Sala de Estar) to sleep the night at, with electricity and and a stove. Even during the day not a bad idea just for a free kitchen and heat. A rare thing to be sure.
Hitching on Isla Grande is relatively easy and people are very familiar with it. Going north to leave you can be lucky and land a truck going all the way to Buenos Aires or farther.