There are lots of labyrinths around Tucson; we can't list them all here. (If you'd like to find others, try the Worldwide Labyrinth Locator.) As Unity's website says, “Unity of Tucson is a Church, School, Bookstore, Wedding Chapel, Health Ministry, and a House of Worship...”
Along the middle of their north-most parking lot (which is graveled) is a sign welcoming you to the labyrinth and asking for quiet. At times when the parking lots aren't emptying or filling, it's definitely quiet.
If you aren't familiar with labyrinths: A labyrinth is a place for meditation… for some people, it's a holy journey. As you walk very slowly around, step by step (it's not a maze; there's only one path through), noticing the details along the way can help make your time there more meditative. For instance, Unity's mural is lined with small colored tiles and some hearts. There's more about labyrinth walking at Walking the Labyrinth: Labyrinth Walking for Spiritual Exercise.
Location: 3617 N. Camino Blanco (south of River Road between Swan and Craycroft), north of gravelled north parking lot
Parking: Parking lots south of labyrinth
Hours: Daylight hours (though it's also magical at night, with a flashlight and city lights in the distance... no other lighting). It's hot out here in the summer, so early mornings or evenings may be best then.