Are there any good backpacking spots close to Boulder?

If getting up to the divide is too much (which is what a lot of the loops in Indian Peaks Wilderness allow you to do), try Golden Gate Canyon State Park. There are some nice beginner options that are still close enough to Boulder that you don't spend all day in a car for a 1-2 night trip. We did our first family backpacking trip this summer, and my 5 year old and 2.5 year old were able to walk the 1.5 miles in to their first "backcountry" campsite. It was fantastic, and there was water available at a little spigot.

My favorite place to backpack camp is the Indian Peaks up past Ned and past Eldora. The area around the 4th of July trailhead has a lot of trails and many can be planed to be a big loop. You can get backcountry permits June-Sept which are free and then camp at the many spots along the way especially nice and near the many lakes in the basin.