Palmer Station is located on the Antarctic Peninsula -- Latitude: 64°46.2′ S
Longitude: 64°3′ W -- and the South Pole Station is located at 90 degrees South.
On the TransAntarctic trek led by Will Steger in 1989-1990, the team walked from the tip of the Antarctic Peninsula beginning in July and reached the Pole on December 12. You can read more, below.
Practically, however, to get from Palmer to Pole, one would fly out of Palmer to South America, north to America, make a connecting flight to Hawaii, then to New Zealand, to McMurdo and to the South Pole.
You can calculate the straight-as-the-crow-files miles using a converter for degrees to miles and come up with about 1,560 miles.
Three research stations are funded and supported by the US government. They are Palmer Station, Amundsen-Scott South Pole Station and McMurdo Station.
The United States of America supports three research stations on the Antarctic continent: McMurdo Station, Amundsen-Scott South Pole Station, and Palmer Station.
If you could fly in a straight line, like a bird, according to Google Maps, you'd fly 7,879.796 miles from Connecticut to Palmer Station, Antarctica.
All science centers in Antarctica are preceded by a [location name] Research Station. Location names can be Palmer, Davis, McMurdo, Scott Base and so forth.
Palmer
4300 miles
You can find:Amundsen-Scott South Pole Station at 90 degrees S.McMurdo Station at 77°50′43.4″S, 166°40′11.2″E.Palmer Station at 64°46′27.1″S 64°03′11″W.
Emilio Palmer is the first person born at Antarctica continent in the year 1978
Palmer Land is claimed by Great Britain, Argentina and Chile.
Actually, Palmer research station is not known for its eating habits. However, people who work there are fed a robust, balanced diet of food brought into Palmer Research Station by supply logistics.
Antarctica is protected by the Antarctic Treaty that, in fact, protects -- and governs -- all of earth south of 60 degrees S. The United States, like governments representing about 80% of the planet's population, supports a presence in Antarctica through work of its National Science Foundation. Three research stations are supported on the continent by USA, including Palmer Research Station, Amundsen-Scott South Pole Station, and McMurdo Research Station.
You can refer to the map, below, to identify those stations that qualify for your definition of 'inland' as locations for research stations on the Antarctic continent.