I visit often with my grandkids who are same age group. They loved going to Dinosaur Ridge near the foothills. http://www.dinoridge.org/ 

Also the Children's Museum of Denver near the Downtown Aquarium is always a hit. http://www.mychildsmuseum.org/

The Denver Botanic Gardens is wonderful and has a kids section. Depending on your budget, the Aquarium is fun but a little pricey, as is the Denver Museum of Nature and Science and Elitch Gardens. If you only have one day to visit, and depending on the weather, the zoo might be best choice

The  Downtown Aquarium is surprisingly good for a landlocked state aquarium.  Liks Ice Cream is good for a treat, and the  Denver Museum Of Nature & Science has plenty of activities for that age range to enjoy, plus it's right next to the  Denver Zoo, so if they get bored of the museum hit the zoo in the same trip. There are ghost tours of  Cheesman Park that don't get too scary, if your kids are into ghost stories.  Elitch Gardens is always a sure bet... hit the  Tattered Cover Book Store if they are readers, and if you can get a little ways west of the city, try  Heritage Square in Golden. Oh, and there's always the  Denver Botanic Gardens (surprisingly kid-pleasing) and especially if they watch South Park,  Casa Bonita is a must-visit for terrible food but a lot of fun.

The Children's Museum of Denver, Denver Zoo, Denver Museum of Nature and Science, Downtown Aquarium, Denver Botanic Gardens, Washington Park, Tea at  The Brown Palace Hotel & Spa in Denver (I used to love doing this with my grandma). All these places have great programs for kids. The Children's Museum might be a bit young for them but the Aquarium is always a hit with any age. 

1. Rent bikes and go on the Cherry Creek Trail and South Platte River bike paths (over 50 miles of paved trail options, mostly flat)
2. If baseball season, go on a Coors Field tour
3. Visit Denver Mint
4. Denver Zoo and Denver Museum Of Nature & Science, right next to each other just east of downtown
5. Go for short drive to the foothills and hike near Red Rocks Park and Amphitheatre
6. Amusement park Elitch Gardens is right downtown

Go to the Children's Museum of Denver, downtown Denver, right off the highway, or for the older child, spend some time at the Denver Downtown Aquarium. You might also want to check out the Denver Mint (though not as fun for kids)

Children's Museum of Denver is a great place for kids to burn some calories.

The best activities are outdoors.

1. Run around Red Rocks Park and Amphitheatre

2. Rent bikes and ride up the Cherry Creek Trail

3. Check out the Alpine Slide at Heritage Square

or.. the Downtown Aquarium is nice.

• Denver Botanic Gardens
  
• Red Rocks Park and Amphitheatre or  Matthews Winters Parkfor light hiking.
• Denver Museum Of Nature & Science
• History Colorado Center
  

Would avoid the Aquarium. It's a hot mess of visitor, especially in the summer.

If they like to ride bikes, the family can rent B-cycles to bike around town on.

Someone mentioned  Liks Ice Cream and I second that. Best ice cream place in Denver. Gets busy and stays busy, especially when the weather is nice, but worth the wait.

Any of the parks in town are great.