Hi -
Okay - I think Breckenridge would be fun. It feels more like a "mountain town" than Estes Park since much of Estes is pretty new, plus the ski lodge is there if your kids are old enough to enjoy SOME of that. You can google it. You may also be able to get a shuttle so you don't have to (potentially) drive in snow.
It may not snow in Denver but there is the zoo, the Natural History Museum, the Forney Museum, and well, that list goes on. There is also the nearby Morrison Museum, if you have someone into dinosaurs. It's pretty much a small house and is very hand's on. The director, Matt, is a pretty famous paleontologist to boot and if he's there, he LOVES to give little kids "the tour." You can also walk Red Rocks as part of that day trip and eat at the Blue Cow in the town of Morrison. Morrison probably doesn't offer enough for kids to STAY there, but it could be a ton of fun for a day. Check out Heritage Square too (in the Morisson/Golden area). Probably the rides will be shut down for winter, but there will be shopping and maybe a play.
Golden is fun and is pretty low key. Not a huge amount for little kids to do, but an easy place to be, downtwon is very walkable, and it's convenient to the mountains and Denver. Also a good one to Google. The train museum is in Golden (you can't walk there though). Lookout Mountain is a pretty easy drive in Golden and the Buffalo Bill museum and grave is worth a look.
If you are more likely to fly into Colorado Springs, go to the Cheyenne Mountain Zoo and feed the giraffes. You might want to go into Woodland Park to the Dinosaur Resource Center (yes, I have had a dinosaur themed life lately). Monarch would be the ski area to check out. Garden of the Gods is not to miss if you are in that area.
My personal favorite mountain town is Steamboat Springs, but that's a hella drive from anywhere, and if you aren't used to snow, you do NOT want to do that one!
If you Google "Kids Colorado" and find some things that look like what you want, feel free to shoot me a message. If we've done it, I'll tell you what I think! My kids are 6, 2, and 11 months.