Table Rock from the Idaho side is a great hike that is around 13 miles round trip and 4,000 vertical feet and the views are outstanding. The first time I made the hike I was 12 years old, but if your kids are too much younger than that I probably wouldn’t recommend.
Edit: just realized you said June and not July. There’d probably be too much snow that time of year for the hike. Be bear aware and packing firearm/spray would be good.