Never quite got to Antarctica due to illness, but did get to Ushuaia to see my boat come back in (and do the Navarino circuit) before heading to El CHalten where we spent 5 weeks.
We spent one hot day walking a long way trying to find one crag while avoiding department of defence signs and failed, and another day making a quick foray into the National Park to do 3 climbs (which probably worked out at $10 each ) by the time we had paid the taxi and entrance fees and the rock quality was reminiscent of Mt Iron in NZ (ie not great ).
El Chalten has excellent bouldering in close proximity to town (and sports climbing including 180m multipitch 5 minutes walk from town). You can hire mats etc easily in El Chalten and shouldnt have trouble finding climbing partners there if in season.