I am heavily indebted to Hoger Gerhardt for posting his example on TeX.SE.

I chose to put a DOI symbol (thanks to the Academicons package) at the end of each bib entry. I think it looks rad.

\usepackage[backend=biber,date=year,doi=true,url=false,style=nature]{biblatex}
\usepackage{fontawesome5}
\usepackage{academicons}
\usepackage{hyperref}
\renewbibmacro*{finentry}{%
   \iffieldundef{doi}{%
      % Entry lacks DOI
      \iffieldundef{url}{%
         % Entry lacks URL and DOI
         \finentry%
      }{%
         % Entry has URL but lacks DOI
         % Show URL hyperlink as icon (concsiously not using same icon as our "external hyperlinks")
         \finentry\space%
         \href{\thefield{url}}{\footnotesize\faIcon{link}}%
      }%
   }{%
      % Entry has DOI \aiDoi
      \finentry\space%
      % lower the DOI  symbol a little to align better with baseline
      \href{https://doi.org/\thefield{doi}}{\raisebox{-0.1ex}{\aiDoi}}%
   }%
}%
% suppress output of DOI field (hide both DOI label and string)
\DeclareFieldFormat{doi}{}%

Here's an example of how the typeset bibliography entries look like (please excuse the poor resolution, the screenshotter suddenly decided to drop the quality):