It helps to think of Denver Union Station as an entertainment complex with a transportation side business. Indeed, it is a microcosm of Downtown Denver in the 21st Century: primarily geared towards downtown employees who want to relax for an hour or two prior to heading home, expense account business travelers, well-heeled downtown residents, and conventioneers. (Also baseball enthusiasts, in season.) As such, it offers little to Amtrak passengers (or ground transit passengers in general) and is not like the legacy train stations in America's larger cities.
There are "lounges" in the station; otherwise known as cocktail bars. Non-dining seating is limited in the station itself and unlike Chicago Union Station or Union Station in DC, there is no self-check luggage storage (though standard Amtrak baggage storage and check-in is available during staffed hours). Off-street parking near the station is non-existent and on-street parking is metered 20 hours/day and often unavailable due to the endless construction.
There is a hotel inside the station, but like many of the other amenities therein, it is out of reach for most rail travelers (much as the hotel attached to Denver International Airport [DIA] is out of reach for many air travelers). Hotels in downtown are consistently in the triple digits and rates stay about the same, even as more hotels come online every year. It is not as expensive as downtown hotels in Chicago or San Francisco, so experienced travelers to those areas may find it 'cheap'. A favorite location of many on this site is the La Quinta Inn on Park Avenue West & 38th Street, about 10 blocks from Union Station. However, I would personally not wish to stay there for more than one-two nights. But it is probably the most reasonably-priced decent lodging in the area.
A better option, if one is flying into DIA, is any of the airport area hotels, all of which offer a shuttle service to/from the airport. This is probably the second or third most economical lodging area (with downtown being the most expensive). Outside of special events and unexpected circumstances, rental cars will also be the most economical in this area. Parking is free and plentiful at almost all hotels (save for the Westin attached to the airport), and rental returns are easy. When you're ready to depart on the train, simply take the light rail A-Line from the airport directly to its terminus at Union Station, on the same tracks that the California Zephyr will arrive and depart from.
Exploring the Colorado Front Range is an easy option as long as one has access to their own transportation. In addition to Rocky Mountain National Park (one of the most-visited national parks in the US), of which Estes Park is the gateway, one can head south to the Colorado Springs area, home to Pikes Peak, the US Air Force Academy and spectacular scenery. An overnight stay in the area will enable visitors to see more and will be quite affordable after Labor Day.
Downtown Denver, once the sleepiest central core of all US major cities, is no longer. Thanks to the bustling convention trade, ever-present construction, and the legalization of recreational marijuana, many of those hoping to benefit from the activity have made downtown their hangout. The 16th Street [pedestrian] Mall is a bustling hub, with a free shuttle which runs the length of the former all-purpose street. However, its activity masks a darker side, with panhandlers, addicts masquerading as performers 'working' for tips, and newcomers hoping to solve life's problems with cannabis populating the neighborhood. As such, though entertaining, it's wise to be on guard when roaming about the extended area.