A day hike on which your friends would have some solitude is the Belly River, in the Park's northeast corner. The trailhead is located just south of the Canadian border station on the east side. Very scenic and they can go as far as they like, then return. Decent fishing (no license needed) and wide open scenery.
The more famous hikes in the Park tend to be crowded in summer, but well worth the trouble.
If they want to do an overnight, camping is restricted to established sites and a permit is required.