Loveland is another place to consider--one hour away from Denver--really super close to Estes Park, which is the entrance city to Rocky Mountain National Park. I am a native of Colorado Springs and Estes Park is my favorite place to visit in the State. You can kill a day in this town and will not want to leave. Lots of fun places to eat/drink, hiking opportunities abound, and you can tour the Stanley Hotel (think Stephen King the Shinning), It can get quite chilly in the park so dress accordingly and if you aren't used to altitude, take it easy. Last time my wife and kids were there, we are driving and we see all these stupid tourist jump out of the their cars and are literally chasing a bull moose through the woods---this is an animal that will kill you to look at you, but they are out there trying to get close for a picture. Just insane.
My daughter will be attending UNC at Greeley and she has her freshman orientation this week. We are dropping her off in Greeley and then spending a day around Boulder/Broomfield and then a day in Estes.
Loveland is just south of Ft Collins and is right on I-25, but you are still only 60 miles from Cheyenne.
I understand Mt. Rushmore may be a bucket list destination for some, but I have been a couple times and it is like, "Wow look at that. (snap a picture) pretty cool (picture from different angle), but that's it. You can take a tour or maybe hit the gift shop. but all in all--not a real interactive place to visit, However should you go up that way, you have to go to Bear County USA.. It is a drive thru animal reserve where the animals are all around you. We haven't been in a several years, but last time, we had a bear rubbing up against our fender and he was moving the whole car. Also price your hotels carefully, last time we went--the cost difference of staying in Spearfish vs Rapid City was significant.
Let me know if I can help with anything else...