In the very S.E. corner is the city of Page (Technically in Arizona) and a whole series of slot canyons - go to google earth and look at some of the pics for "antelope canyon" there are several of these slot canyons other than upper/lower antelope contact a guide on the web. After a Bryce/Zion which are also "Musts" I think the slot canyons are as well. Take at least a monopod on the shoot, there will be lots of slow shutter speeds. Antelope Canyon is on the Indian Reservation and plan to get there well before noon and you want the "tour" closest to noon or the sun zenith to get the best light penetration.

Utah has some of the most impressive landscapes around. Grand Canyon is not far away, but after Bryce it is just another giant hole in the ground - worth it if you have the time, but if pressed for time I would do Bryce/Zion and the slots the greatest variety.