Have you been to White Ranch Park or Reynolds Park? They both have designated campsites 1-3 miles in, depending on which trailhead you start from. White Ranch in particular is very close to civilization should something not go as planned.
You could also go to Staunton State Park. It’s basically car camping but you hike in a little ways. That’s about an hour from the city.
These are both reservation-based designated campsite type places. The Mount Evans and Lost Creek Wilderness areas are also kinda sorta an hour from Denver. Maybe start at the Brookside-McCurdy Trail or Ben Tyler Trail off 285? Or the Wigwam Trail? Someone else here with more knowledge could fill you in on if these or other spots in that direction would work for you.