Simple Recommendations For Visiting Denver

I would recommend visiting Rocky Mountain National Park, its a beautiful and huge place only 1.5 hours from Denver. It has many great hiking/climbing areas and awesome views. Although there will be tourists there it's a big enough place that you will find solitude and enjoyment there any day of the week. 

There is also Mount Evans also only 1.5 hours from Denver, it's a 14,000 ft. mountain that you can drive to the summit of and see for miles and miles almost the entire state of Colorado from! Tourist activity on Mount Evans will be much lower on weekdays, so plan to go then. There are also the Denver Mountain Parks, all within 45 minutes of Denver in the foothills. They offer great hiking and views of the mountains. On your way to Rocky Mountain National Park you might consider stopping in Boulder. Boulder has lots of great restaurants and a unique outdoor environment.

Here is the website for each of these:
Rocky Mountain National Park - Rocky Mountain National Park
Denver Mountain Parks
Mount Evans - Highest Paved Road in North America
Boulder Colorado
Hikes in Boulder

There are several great museums in Denver. There is the Denver Museum of Nature and Science, a great place with many awesome exhibits and artifacts. They also have a different main exhibit every few months so make sure to check if what is currently exhibited interests you. There is also the Denver Art Museum, another large and great museum with many forms of Art by famous artists.

Websites:
Denver Art Museum
Exciting minds of all ages through scientific discovery : Denver Museum of Nature & Science

There are many great restaurants and breweries. I would suggest going to Wynkoop Brewery it has good food and a great Bar. There is also a restaurant in Golden just 10 miles west of Denver called Old Capitol Grill which has great food.

Websites:
Wynkoop Brewing Company
Old Capitol Grill in Historic Downtown Golden, Colorado
Denver's Best Local Restaurants - Taste Colorado's Cuisine | VISIT DENVER

As far as walking, Denver has great parks and walking trails. There are parks in Denver and the surrounding suburbs as well as the foothills, and all are great for walking. 

Info on parks in Denver
Denver's Parks

Hope this all helps, and have a great visit