The quick answer to your question would be the Granite Dells, situated 5-6 miles north of downtown on both sides of Hwy 89a. They are perhaps 10 sq miles of pretty unique pre-cambrian granite weathered formations, with two enclosed lakes (Watson and Willow) for drama and wildlife. Much of the Dells is private (including my 10 acres!) but the City of Prescott owns the two lakes and maintains them along with adjacent trails. Start with the Watson Lake park at 89a and Willow Lake Rd. A lovely rails-to-trails that traverses the best of the Dells is the Peavine Trail. Trailhead is at Sundog Ranch Road off Prescott Lakes Parkway. Peavine is some 4-5 miles long, wonderful rock formations are near the old junction of Entro at about 3.5 miles.
Prescott is in a north-facing bowl of the Bradshaw Mountains. Downtown is photogenically historic (at least to Arizonians). Literally hundreds of miles of Prescott National Forest trails are near. Great hiking, e.g. Granite Mountain Wilderness.
As Quentin said, the "ghost town" of Jerome is 45 minutes up Hwy 89a and both interesting as well as photogenic. Lots of old buildings sliding down the hill, good galleries. Make a day trip of it and continue 30 minutes on to Sedona, which is really pretty and really popular. An intimate, accessible cliff dwelling near Sedona is Palatki. One of the best petroglyph sites in Arizona, V-V Ranch along Wet Beaver Creek, is just a couple of miles east of the I-17 and Hwy 179 (to Sedona) junction.
If the friends you are visiting have a high clearance 4x4 then the backroad possibilities are numerous.
Lastly, know that the Grand Canyon Park is just 2 hour and 15 minutes away!
Hope you enjoy your visit.