Taking light rail from airport to downtown Denver is a safe bet lots to do way more than you can on short layover would recommend getting off 16th St mall for dining maybe check out Rino district .
16th Street Mall has everything, including free transportation up and down the road. And one can take the A Train to and from the Airport
Well, if you could be a little bit more specific as to what you're interested in, especially with dining, I might be able to recommend some places.
Google: shopping in Denver area
I would say Boulder as well
Boulder or downtown denver have plenty of great options for both
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