Arequipa doesn't have sheer number of the "must-sees" of Cusco and the Sacred Valley or Peru's Coast. (Personally, I'm not fond of the term since people's tastes vary and I don't think of travel as a competitive activity). However, next to the Monastery of Santa Catalina, the attraction that appears to be worthiest of the title (certainly in terms of popularity) is the nearby Colca Canyon. Nearby is a somewhat relative term, since it's approximately four hours away by road, the first hour over the smoothly paved thoroughfare that also runs to Cusco and Puno, the next over tortuous dirt roads, and the final two over a winding cliffside path that might be described as combination between the two.
It's theoretically possible to visit the Canyon's highlights in a single day via a tour from Arequipa. However, "day" might be stretching it slightly as you have to leave at around 3 am and arrive deep into the night, hours at both ends seemingly used only by airport departures and arrivals and nocturnal revelers. A more sensible approach, which I followed, is to take a two-day tour which picks you up around 8 am one morning and drops you off the next evening at 5 pm. The price isn't much higher (although it rarely includes any meals besides a rudimentary breakfast) and the pace is slightly more relaxed. If you're particularly physically fit and don't have problems at high altitudes, several friends of mine have spoken highly of a 2 or 3 day hike in the canyon - but while I'm an enthusiastic hiker the altitude (which can reach 4,500 meters in some places) was a bit much for me so I'll have to pass this along as hearsay. You can also go by public transportation, which is safe but only a little cheaper than if you arrange the trip through a tour agency and means you have to work out travel between the points of interest in the canyon which is difficult without your own vehicle since the only local taxis I saw were of the tricycle variety.
Regardless of how long you go for, your itinerary is likely to include some mixture of photo opportunities, hiking, watching wildlife, and seeking to appreciate local culture by visiting the valley's colonial churches and perhaps watching local dancers (who are often to be found outside said churches). If none of these appeals to you, I doubt the canyon would - but if any of the first three do it's well worth the effort of going. Before doing so, however, make absolutely sure you have spent time to get acclimated to the altitude in Arequipa and pack alcohol, cotton wool, and some altitude sickness pills. Any reputable tour agency will either have these or stop en route to pick them up, but I can't stress strongly enough how important they are since fully half of my tour group succumbed to altitude sickness in some form or other. The canyon is very cold at night and scorching in the day, so plan accordingly with a jacket, a good hat, and lotion.
In my opinion, the Canyon's two most emblematic animals are vicuñas (shy wild relatives of llamas and alpacas) and condors. Technically speaking, you won't see the vicuñas in the canyon but rather on the way. While shy they often stop photogenically by the road and their enormous black eyes and plaintive expressions are quite different from their more circumspect and aggressive domestic cousins. Their wool is the finest in the world and they were nearly hunted to extinction because of it - today they're recovering in numbers and are occasionally rounded up and sheared. Condors, which you'll likely see in the Canyon itself at the so-called "Cruz del Condor" (Cross of the Condor) are among the world's largest flying birds and have been used since time immemorial in South America as an important symbol of power. Other animals you may come across include vizcachas (long-whiskered rabbit-like rodents), flamingos (on the way to the canyon) and Andean ducks.
The extent of photo opportunities and hiking will depend on your trip and guide. At the least you'll have the chance to clamber along the canyon's side near the Cruz del Condor for an hour or so (as I did), while on a longer hiking specific trip you can go deep in the heart of the canyon itself. Despite the relatively dry climate in the canyon and around Arequipa generally, it has be farmed for centures by the Collagua and Cabana peoples. The brightly colored hats worn by their women serve to distinguish them from one another as the Collaguas wear one type and the Cabanas another - before the Spanish conquest this distinction was achieved by cranial deformation.
The churches that dominate the main square of every town in the valley are the most potent reminder of the Spanish presence. So too are the local dances, which you may well be treated to in front of these churches which were in many cases intended as subtle criticisms of Spanish rule. The presence of a single dancer who breaks free from the group and carries a pot to tourists in search of donations is a more recent innovation, as are women who have tamed hawks and eagles and will let you pose with them for a fee. Many of the towns in the canyon, especially Chivay, the capital (which is actually just outside it) have nightly performances of these dances where you make payment a bit more directly and beforehand.
For many years, Colca's claim to fame was as the world's deepest canyon, twice as deep as the Grand Canyon, although scientists have since found that the nearby (but difficult to access) Cotohuasi Canyon is actually slightly deeper. Stripped of this superlative, Colca is a pleasant enough place to visit, and an agreeable place for a change of pace from Arequipa. While the presence of wildlife that I had not previously seen was a highlight for me, I was not as impressed by the scenery as I was by the Sacred Valley near Cuzco and I would personally hesitate to label Colca one of Peru's natural highlights. It's certainly worth seeing if you're near Arequipa, but I don't think it's worth going out of your way (or risking altitude sickness if you're susceptible to it) for.