Day hiking:
Colca Canyon is ideal for day hiking.
You could simply book a 1-day tour out of Arequipa (about US$23), but that is far too rushed. Requires far too much driving in one day. Some tours leave at 3AM!
You could book a 2-day tour (starting about US$30) which is better (depart Arequipa at 8:30AM, return about 6:00PM the next day). But this website is for independent hikers who would rather arrange their own travel; it is cheaper & can be more fun.
We recommend you travel independently to stay in Chivay (3700m), or even better Cabandaconde (3290m) & day hike from there. Public buses from Arequipa are convenient <details>.
The entire canyon rim between Chivay & Cabandaconde is fascinating. You could do various sections over a couple of days, returning to your hotel or hostel each evening.
But the best single viewpoint is Cruz del Condors where you have a chance to see a nesting family at close range; eye level or from above. This is a fabulous & unique experience. This spot is likely the best place in the world to see condors, one of the largest birds anywhere.
That said, perhaps the best day hike of all is the stretch between Cruz del Condors & Cabanaconde, 2-3 hours. Stay in Cabanaconde. Take public transport to Cruz del Condors to arrive by 7:30 AM (the tour groups arrive about 8:30 AM) & walk back to Cabanaconde before it gets too hot. Walk the aquaduct rather than the road.
Some in your group may prefer to do day hikes while others do the 2-day hike into the canyon. There is something for everyone in Colca Canyon.