The beautiful city of Arequipa is 1000km South of Peru's capital Lima (best to catch a flight). The city has been declared a UN World Heritage site, and has many fine colonial buildings, churches and cobbled streets to explore. The Santa Catalina Convent is the top travel highlight of Arequipa - an amazingly beautiful walled colonial city were 400 nuns used to live in seclusion.
Arequipa's surrounding countryside offers some lovely hikes - to climb the nearby El Misti volcano is not an overly challenging task. The town is worth a few nights as a travel base, but many people choose to catch a moning flight from Lima and spend just one night (visiting the Santa Catalina Convent on their first afternoon), before travelling on to Peru's amazing Colca Canyon.
Top of the range hotels in Arequipa include the Libertador Ciudad Blanca or the Sonesta Posadas del Inca (though neither could be considered genuine luxury hotels as are found elsewhere in Peru).
Travelling overland from Arequipa to Lake Titicaca through the Colca Canyon can be comfortably done in a couple of nights. Basing your Peru travel itinerary as such allows you to slowly acclimatize to the heights of the highlands.
The deepest canyon in the world, the Colca Canyon offers some of Peru's most spectacular Andean scenery. There are numerous small and picturesque Andean villages in the Canyon, as well as some fantastic trekking opportunities. One of the most popular activities is to visit the Cruz del Condor, to see the majestic Condor bird at close quarters (May to December being the best time to see these monstrously huge birds). There are also hot springs in the Colca Canyon, but the principal travel attraction is the outstanding mountainous scenery.
As for luxury hotels in the Colca Canyon, the remote Colca Lodge is the best option. It may well be fully booked (it often is) - the best alternatives include the Estancio Pozo del Cielo or the Casa Andina Hotel (both in the town of Chivay), or the Orient Express owned Parador del Colca.
It's possible to visit the Colca Canyon as either a day tour or an overnight package from Arequipa, but there's little point - you might as well travel all the way through the canyon to Lake Titicaca.