This tower is in Taylor Canyon, between Moses and Aphrodite. Zeus is a little more serious then Moses, but has good climbing, good rock, and is a good half day outing.
Getting There
Walk up the trail past Moses to Zeus.
The Classics
Mountain Project's determination of some of the classic, most popular, highest rated routes for Zeus:
Sisyphus 5.11 R Trad, 3 pitches, 250 feet, Grade III
First, regarding the Northeast Ridge: I'm not sure what's more lame, chopping a route or drilling one up a completely blank face with no regard to natural features. Right now, all the bolts (except the anchors) have been chopped (not pulled) and it is an ugly mess. If anyone were to replace them (which they shouldn't), perhaps they could at least be moved a little to the left near the arete -- this feature might actually be free climbable.
Second, because the anchors are still intact, it is possible to rap Zeus with a single rope.
Finally, I think the rack recommendation for Sisyphus may be a bit excessive for free climbing. We brought the recommended rack and never used the 3.5 Camalot, or any doubles (let alone triples) of any of the cams except the 0.4 Camalot/Yellow Aliens. A single set from black Alien to #3 Camalot with extra yellow Aliens would be fine. Wires are nice for the pin scars, however.
I've added a photo of the two first ascenitionists that is from the Museum of Moab. It was taken by Fran Barnes. The museum also has one of one of the two guys just about to summit. Its from afar and you can see the dust on the rock near the new bolts. I think we need to keep in mind that desert climbing required a different mindset then. There were no large cams to utilize when going up the crack, etc.