A function of a list of, say, 100 cities, and we want the FURTHEST point in the Continental US

Assuming the answer to my comment is yes, here is one way to do it

polygonUS = Entity["Country", "UnitedStates"]["Polygon"];
borderPoints = polygonUS[[1, 1, 1]] // Map[GeoPosition];

furthestFrom[city_, borderPoints_] := 
  AssociationThread[borderPoints -> Normal@GeoDistance[borderPoints, city]] //
  ReverseSort // Take[#, 1] &

london = Entity["City", {"London", "GreaterLondon", "UnitedKingdom"}];
furthest = furthestFrom[london,borderPoints]

<|GeoPosition[{32.5343, -117.124}] -> Quantity[5504.35, "Miles"]|>

furthestPosition = First@Keys@furthest;
furthestCities = GeoNearest["City", furthestPosition, 2]

{Entity["City", {"ImperialBeach", "California", "UnitedStates"}], 
 Entity["City", {"SanDiego", "California", "UnitedStates"}]}

GeoGraphics[{Red, GeoPath[{city, furthestPosition}, "Geodesic"]}, 
 GeoRange -> {{10, 70}, {-120, 10}}]

I continued to fiddle around and came up with this, San Francisco is just an example. In this case, it looks like Mahchester, NH is the furthest to San Francisco.

cityCenter = Interpreter["City"]["San Francisco"]
cities = CityData[{Large, "United States"}];
table1 = Table[{cities[[k]], 
    QuantityMagnitude[TravelDistance[cities[[k]], cityCenter]]}, {k, 
    Length[cities]}];
First[Sort[table1, #1[[2]] >=  #2[[2]] &]]