Having Uber or great public transportation will not change the fact that much of the draw of Colorado is that you can drive two hours and end up in the mountains or on the plains. Colorado self-selects for cars and they will not be going away any time soon.
That said, once a car isn't needed for day-to-day life in multiple neighborhoods in a city, and likewise once relaxed parking space requirements make it such that keeping a rarely-used car isn't trivially easy, (and especially an economy where reliable used cars have become far more valuable and unnecessary line-items in the budget might be quickly removed) the economics for young adults tilt pretty heavily toward tossing in gas money to with your car-owning friends or renting a car for $100 every few weekends when desiring a trip to the mountains. And urban families might become one-used-car-kept-for-10+-years families as opposed to one-car-per-adult families.
My understanding is also that Denver has a pretty-decent network of bike trails and a relatively-mild climate, which also means two-to-five mile trips can be pretty easily covered without a car.
Of course Denver won't become New York— but it stands a chance of becoming less of an auto-required city and more like the DC area, which is a relatively young metro area for the East Coast with a mass transit system from the modern era and new urban nodes at outer transit stops, and many people still own cars but plenty don't, especially in the urban core.
As a side note - can't you drive two hours to a mountain from most East Coast cities? The Catskills are only 2.5 hours from NYC. I thought mountains were much more accessible in Denver than a two-hour car ride.
I wonder if the rise of Uber will affect this.
When I lived in Seattle, I noticed that a lot of people didn't commute to work via car but had one anyway, usually for one or two trips per week. Public transportation (buses and later light rail) were pretty good from about 8 a.m. to 7 p.m. or so during weekdays but were horrible the rest of the time. Bikes could be used intermittently.
Uber does an amazing job of filling in the gap. Last time I visited Seattle, I was struck by how some of my friends had given up cars, despite rising incomes, largely due to Uber. Uber may play a key role in getting rid of a lot of cars that are only marginally utilized, since it appears far more reliable and friendly than taxis—virtually all Seattlites who have to use Seattle taxis hate them. This has environmental and other implications.