GC Caverns is worth the stop. Very good tour. There is even a hotel room built deep inside the cavern albeit very expensive.
While inside the caverns remain cool, outside during the summer months can be rather hot. A better choice would be to stay at Grand Canyon Railway RV park in Williams and make a day trip to the caverns. Not far from the caverns is Keepers of the Wild animal sanctuary that's a fun stop.
Williams is at 7,000 feet and is in the cooler forested pines. In Williams is Bearizona drive thru animal park and walking zoo. Well worth a visit. Theres also a deer petting zoo nearby thats fun.