Take 77 south from Holbrook to Show Low and then 60/77 south to Globe. From Globe southwest on 60 will take you to the Apache Junction turnoff and on into Lost Dutchman. You will love Lost Dutchman SP, one of our favorites. Lots to see and do in the area and still close enough to hop on into Phoenix should the need arise.
Another somewhat more scenic/rural route is go south on 191 off of I-40 at Sanders down to Eagar. Pickup 260 west at Eagar over to Show Low. You will do some climbing, up over 9,000' but the road is good and the scenery is awesome. Neither route will pose any problems for your rig.
Here is a shot taken at LDSP, bring your hiking boots!