There is no beer in Colorado...
Just kidding. Denver is packed with places to go- at least 150 breweries in the metro area. A great place that is close to the airport is Dry Dock, the "North Dock" location is only about 5 minutes away from you. Station 26 is pretty close also makes some great beers.
Ursula (formerly Coda) and Fiction are also close to you.
If you venture downtown, I can recommend Epic, Great Divide Barrel Bar, Ratio, and Former Future. If you like Sour Beers, you must try Crooked Stave- can get a bit pricey. River North is another good one, just a bit North of downtown.
In the South Metro area, Bull and Bush is an English style pub that makes great beers. Comrade makes great beers.
TRVE is a death metal themed brewery with good beers and a black vibe.
If you like hoppy beers, Odd 13 is great to check out, in Lafayette, about 30 minute drive away.
If you really want to commit to it, Avery is the best place to visit in Colorado IMO. (~45 minutes away)
They have a rowdy bar downstairs and a nice semi-upscale restaurant upstairs, 32 taps, all of them are Avery beer. They run the gamut from light lagers, sour beers, heavy dark beers, experimental brews, and hoppy styles.
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For taprooms, there are a lot of choices.
Falling Rock Tap House is famous, they have bar food and great beers.
Freshcraft has modern food and a good tap list.
Lucky Pie, World of Beer, Yardhouse, Tivoli, Euclid Hall, Star Bar, First Draft Alehouse...
And there's even more. I can also recommend bottle shops if you want to take something special home with you.