TXHunter nailed it. Elk will be where you find them. They'll move based on food, water, cover and most importantly pressure. I know 2 different places in Colorado where I watch elk summer and calve in remote alpine basins. The older bulls are even further back in harder to reach areas. When September comes the cows move down the drainage into timber pockets very close to major roads, people and communities and the bulls come to them. I still see a few animals lingering in the high country but most have moved down. People drive by them all day long driving to the major trailheads. You could stay in a hotel and hunt these animals as effectively as you could pack in and camp.
Also keep in mind that there are limited entry units and statewide units for most elk hunts in Colorado. Muzz hunting for elk is by draw only. If the unit has an elk season and there's no specific hunt code for that unit's muzzleloader season hunt then it is probably covered by the general statewide muzz tag. That being said there are some units that are limited for some seasons but not all seasons. For example some units in the white river national forest have a limited entry archery and muzz season but are general rifle units. Read the regulations and call the DoW if you have any specific questions.
For an over the counter hunt I'd spend more time concentrating on enjoying being out with the sons than having a solitary elk hunting experience.
will