Haven't been to Frontier Days, but have been to Cheyenne a couple of times to visit a family member stationed at the AF base there. If you like outdoors stuff, head towards Laramie and visit Vedauwoo for some cool rock formations and rock climbing if that is something you like. There are a number of fairly easy trails as well. Head through Laramie and go to Medicine Bow-Routt National Forest if you like hiking. There are a number of fairly easy trails and Medicine Bow Peak tops out at 12k. Even if not a hiker, it's a nice drive.
I remember eating at a place in Cheyenne called Wyoming Rib & Chop House that I thought was pretty good.
If you go to Mt Rushmore, be sure to drive the Needles Highway in Custer State Park. Sylvan Lake is pretty cool too. Badlands is really unique. I thought Rushmore and Devil's Tower were kinda 'meh' (may be partly due to the crowds), but something I wanted to see with my own eyes.
I know this doesn't help with your Frontier Days question, but maybe it helps in finding other things to do!