The highest point in all Antarctica is Vinson Massif, now famous as one of the "Seven Summits". Sometimes referred to as "Mount Vinson", it is named after a U.S. congressman from Georgia who was friendly towards the Antrarctic reseach programs during the International Geophysical Year of 1957, when the peak was discovered and mapped.
Mountain guide comapies run trips to this frozen, isolated peak in the West Antarctica interior every year, charging clients tens of thousands of dollars per person. The climbing is reportedly easy, ignoring the bitter cold and ridiculous logistics of getting yourself there. The usual method is to use a cargo plane with ski landing gear, leaving from southern Chile. Only a cargo plane has the necessary range for the flight, and basecamp is set up on the smooth ice cap to the west of the Sentinel Range.
Info from Mike Sharp at Antarctic Logistics and Expeditions Llc: We now run an almost
weekly scheduled flight to Patriot Hills Antarctica using an IL-76 jet, which is a cargo
plane designed and built for landing on gravel strips in Siberia. It is ideal for
the job and lands on our ice runway on wheels. Passengers are then transferred to
Vinson Massif by ski equipped Twin Otter. The climb is of similar difficulty to Denali
West Buttress, but several days shorter--most parties take about 14 days round trip from Punta Arenas, Chile.