Denver, the most populated city in Colorado, and most travellers' airport of arrival, is as flat as a cowboy's pancake. This makes cycling around the city a pleasure while the weather holds. On colder days, you can visit the State Capitol, which, with its golden dome, is a mini-version of the real (national) thing in Washington. There is a superb view of the city lying in splendour from the front entrance. The view from the top of the dome is even better, though the opening hours (9am-3pm, weekdays only) are inconvenient.
Art and culture abound in this city. The Denver Art Museum (closed Mondays) has a surprisingly excellent (and inevitably huge) collection of Native American art. Countless bands play local venues; the university has a great theatre (but go with a full petrol tank - it is impossible to find). There's even a good IMAX (3-D) theatre, or so I hear - a similar experience in Alaska caused me such disorientation that I had to run outside into minus forty degree temperatures and throw up.
Don't take your small children. Take them instead to the planetarium or the zoo. Or to one of the state's many disused mines (and leave them there).
As an escape from the big city, the attractive town of Boulder lies on a plateau tucked into a mountain range. The University of Colorado, with its 2,000 students, is located here, and keeps the average age of the population to adolescent figures during term-time. The main shopping and dining area around Pearl Street Mall is filled with a zillion cafes, restaurants, and gift shops.
From Boulder, it's a solid hike to nearby canyons and panoramic mountain views. It is also a short drive to The Rockies, and the scenic Trail Ridge Road, which crosses the Continental Divide as it leads up to an elevation of 12,000 feet through alpine tundra. The road has frequent parking areas from which marked trails into the mountain landscape begin. But be warned - do not stray from the path, Little Red Riding Hood, or the wolves will get you, otherwise known as fanatical American environmentalists who pop up if you so much as breathe outside the designated track and scream abuse (not the most pleasant experience of my holiday, I can assure you).
In spite of all the many warning posters, the famed last-existing grizzly bears don't, in my opinion. Although other varieties do exist, and will eat your dinner if you camp out overnight (note: hiking permits required).
Elk, bighorn and moose can often be spotted nibbling shrubs, though most movement perceived through binoculars will turn out to be exhausted schoolchildren being shepherded back to base by weary Rangers.
Aside from hiking, you can cross-country ski, mountain bike or cycle, white-water raft, rock climb, canoe or kayak, all depending on the season, in any of Colorado's national parks. This is truly America's Great Outdoors.
Bungee jumping is not legal so I won't mention any possibilities - if you want to (and will pay) enough, you'll find the way. Helmets should, of course, be worn for all the above activities.
About 100 miles south of Denver, on the other side of all the major ski resorts and in the heart of red rock country, lies the town of Colorado Springs. From here, there is a road that leads up Pikes Peak to a 7,000 foot plateau. It is popular to mountain bike down from the summit, but the morning I went up, a teenager shot off his bike and free-fell several hundred feet, from where it was a slow and difficult process to engineer a rescue. This is not a rare occurrence. I wouldn't whizz 7,000 feet down a mountain on a fast-moving projectile, but then again, I don't ski.
Finally (due to space rather than activity limits), I recommend a trip into Red Rock Park to see the superb natural beauty of the towering stone formations.
This area is known as "The Garden of the Gods", christened by an explorer long since forgotten, but equally applicable to most of the territory in this, America's most famous South western state.
Of course, when winter blizzards hit, stay in the chalet and get sloshed along with the best of them.