The Botanical Garden's one of my favorite places in Phoenix. It might be a little expensive in some peoples' minds, but I find the plants fascinating and relaxing enough that it's more than worth it.
My favorite times to visit are during the late spring and catching the cactus blooms, or a rainy day in the winter. Sometimes if I know it's likely to rain I'll see if I can squeeze in a visit, because you simply can't top the way the smells of the desert and the plants come alive when they get hit with a good shower.