Here's what I'd pick if I were faced with free time in Arizona:
Flagstaff Extreme - If you were planning to do more than just look at the Canyon, odds are you're something of an action addict. Put those muscles to work at Flagstaff Extreme instead, a public-private partnership that allows visitors to swing through the trees on increasingly difficult obstacles. It's a unique challenge you won't ever forget. It's right off the I-17 and I-40 - more details at http://www.flagstaffextreme.com.
After you conquer all four levels of the obstacle course, or if you're looking for a more relaxing approach to the region, enjoy downtown Flagstaff - it's the perfect combination of college town, tourist center and community.
Arizona State Parks - With no disrespect to the Canyon, our state parks are amazing...and there's no doubt they'll be open tomorrow. They're spread across the state so there's a state park close to wherever you are - check out their website (http://azstateparks.com) for more information. My favorites: Boyce Thompson Arboretum for a quiet stroll, Dead Horse Ranch for close-to-civilization camping, Kartchner Caverns for jaw-dropping underground excitement (reservations required), and Tonto Natural Bridge for good, old-fashioned appreciation of natural beauty.
Lake Havasu City - If your plan was to party at the Canyon, head farther west to Lake Havasu. There's excitement of all kinds, at all hours whether you want water sports or casinos.
Speaking of Casinos - They're everywhere in Arizona. Chances are that wherever you are, there's a Native American tribe that is eager to play host and show you the best food and games their casinos can offer. Plus, you'll be doing good since a portion of gaming revenues go to non-profits in Arizona each year.
San Xavier del Bac Mission - This remnant of Arizona's fascinating history is a great place to feel for more information on tours and Catholic services.
like you're a part of the past. It's the perfect stop along the way to other Arizona adventures. Check their website (http://www.sanxaviermission.org).
Sonoita - It's a long way from the Grand Canyon, but when you get there you'll think you drove all the way to Europe...or at least Napa. These sloping hills of vineyards are straight out of a postcard, and so is the award-winning wine. There are many to choose from, but be sure to include Hops & Vines on your journey - it's a unique place owned and operated by two sisters who are more lively and interesting than any reality TV show.
Prescott - I'm biased because it's my hometown, but I think I saved the best for almost-last since Prescott is truly unique. Read a book in the city park at the center of town, shop at boutiques for beautiful art and silly souvenirs, or hike at one of the mountains on the edge of town - it's not called "everyone's hometown" without cause. Be sure to grab coffee at Wild Iris, my favorite place to meet locals or just enjoy time to myself.
Phoenix - It's the state capital, the business center and increasingly the urban hub of nightlife and outstanding dining and entertainment. There's something for everyone, and Downtown Phoenix Partnership has all the information you need. They also provide orange-shirted guides throughout downtown Phoenix, so feel free to pester them with questions.