As has already been said, you can do Elephant hill, and maybe even stay in Devlis Kitchen (cool place)...
maybe even do the hike in Chessler park...
From there you can take the trail out the back into Beef Basin, and explore a bunch of cool Anasazi Ruins... a cool way to see some remote back country..
Another option is to head south past Blanding and do Hotel Rock... some tricky climbs, so better to be with someone.
and if you choose to go north from Moab, you can take back roads to some cool Dunes and canyons to explore on the way to the San Rafael Swell... more of the swell than can really be explored in a week..... but a week would be really fun.
1996 - FZJ80 (supercharged)
1985 - 4Runner (Squeaky Toy)
1976 - FJ40