Arches National Park is tremendously beautiful and quite interesting - check out the pictures below for a better sense of it than my words can convey. As the name suggests, Arches is replete with huge stone arches carved out over the eons by the elements. It has loads of beautiful hiking paths of varying difficulties (and unfortunately loads of tourists as well, but if you get there early or you go off on less common trails you can avoid most of the crowds). On our first night we met a Hawaiian helicopter pilot named Josh at the overflow site, and we hiked with him most of the day after. Cool guy.
Canyonlands is, as its name suggests, is full of gargantuan canyons and cliffsides which are impressive to behold. You can see canyons within canyons with even smaller canyons inside them... it's almost fractal. It's farther away than Arches from Moab but well worth the trip, and has far fewer visitors. We also visited Valley of the Gods and Natural bridges, which are both great but only if you have the time and the stomach for the drive there - it requires a steep ascent of over 1,000 feet over narrow dirt road switchbacks, which afford you some amazing views of the valley below.
Moab is a pretty cool city. We liked it much more than Sedona and Kanab because it felt intelligent and fun without being pretentious or trying too hard. We stayed in the area for about a week. There was a jeep rally there which was fun to watch - jeeps jeeps jeeps everywhere. Lost River Coffee makes a great americano, and the natural food store across the street actually has great food at reasonable prices.