How to best visualize data when outliers lead to lack of contrasting colors for the rest of the plot?
With Wolfram Language you may use GeoRegionValuePlot with the ColorFunction option to customise the colour scaling.

With some "AdministrativeDivision" "Population" data for the Philippines.

popPH = EntityValue[
   Entity["Country", "Philippines"]["AdministrativeDivisions"],
   "Population",
   "EntityAssociation"];

First@Normal@popPH



  


Then GeoRegionValuePlot with and without a custom ColorFunction.

linear = GeoRegionValuePlot[popPH,
  ColorFunction -&gt; ColorData["SolarColors"],
  PlotLabel -&gt; "Linear ColorFunction",
  PlotLegends -&gt; Placed[Automatic, Below]
  ];

log = GeoRegionValuePlot[popPH,
  ColorFunctionScaling -&gt; False,
  ColorFunction -&gt; (ColorData["SolarColors"][
      Rescale[Log@#, Log@QuantityMagnitude@MinMax[popPH]]] &amp;),
  PlotLabel -&gt; "Log ColorFunction",
  PlotLegends -&gt; Placed[Automatic, Below]
  ];

Row[{linear, log}]



  


Hope this helps.