It depends on where you are staying. If you are staying in a hotel vs. a house it might work. If you are staying in a hotel where you will be picked up for excursions (or can walk to pick up point) to the Grand Canyon and for the Pink Jeep tours that will work. If you are staying at a hotel on the main drag you can walk to the stores and restaurants. Other than that it might be nice to have car to drive around and enjoy the majestic scenery. A week is a long time and you don t want to end up getting stuck sitting in your hotel room watching tv.
A car will be beneficial to you while visiting Sedona. Tours are fine, but it s nice to have a vehicle to explore the area on your own. Especially if you ll be here for an entire week.