I lived in Crown king for two years, I'm in Prescott now. Figured I'd start with something easy first. The Liberty is stock height so
Aww man there is so much dirt to explore in your neck of the woods. I love spending time up there. If I could find work I would move to the Prescott area.
Senator highway to CK is what I would suggest. Not sure if it has been raining up there like it has in the PHX area but if it has I would wait a few days until it dries out. Seems that whole area turns into a mud pit with any rain.
Prescott to CK then head out on the Goodwin - Mayer highway to Mayer to head on back via the 69.
Not sure if that is old hat for you since you lived in CK but it makes for a nice day and there are plenty of side roads if you are feeling adventurous.
Last suggestion would be to head to Mayer and take FR93 (Blue Belle Mine Rd) down through the Blue Belle Mine area into Cleator. Then you can head home anyway you please. A stock KJ should have no problems; only one or two off camber corners and one rocky section IIRC.
Try to wheel with at least one other vehicle if you can. If not make sure you have recovery gear, lots of water, and tools if you plan on trekking solo. I rarely ever see anyone else on some of the lesser known back country roads.