Garden of the Gods is free and is a good way to spend an hour or so if you are willing to walk a little bit. Really incredible place. Ive dont a jeep tour there which is fun for the kids and you learn more about the history of the place.
Pikes Peak is pretty cool, the train is the best way to get to the top. Its pretty expensive though. If you want to avoid the millions of tourists and pay a fraction of what it costs to go up Pikes Peak, while still being able to drive to the top of a 14er, go to Mt Evans near Denver. Its much more worth your time IMO. And its only $10 (free with a National Park pass) as opposed to $40 for Pikes Peak. There are also way less people on Mt Evans, and its surrounded by more mountains so its a better view from the top.
Cave the Winds is a fun place for kids to be able to see a cool cave (famed home of Man Bear Pig). Its right next to Garden of the Gods. Right next door is a bunch of Native American cliff drawings and petroglyphs.
Manitou Springs is a must if you go to the Springs. Its an old town up against the mountains (right near Garden of the Gods and cave of the Winds). Really cool town with tons of restaurants and shopping and old buildings. Great place for Dinner and a stroll around town.
Air Force Academy is great too, but kids may not like it as much if you have them. The Chapel is incredible and its cool to see the Parade Grounds too. Its free but security checks your truck of your car quickly. There is a neat museum there too to show how the cadets live and with history exhibits.
The US Olympic Training Center is there, havent been to it but I think they do tours.
If you are into military related things, the National WW2 Aviation Museum is in the Springs as well.
Victor, Colorado isnt too far away and is an old mining town, there are a bunch of old abandoned mines you can walk around and see how they used to do things.
Royal Gorge near Canon City is really cool but its kind of a tourist trap and a bit expensive. If you are ok with that, then you will enjoy it. There is rafting through the Gorge too and many other places along the Arkansas River.
If you are ok with a little bit of a drive, Great Sand Dunes National Park is one of the most unique places in the world. Huge sand dunes up against snow-capped mountains. Really neat place to explore. There are slides and things you can use to slide down the sand dunes. Denver is close by too obviously.
Plenty of good food and breweries in the Springs, as well as Denver. Let me know if you have any other questions!