Peak blooming season is generally mid-March through April.
There's a list of colorful areas in and around Tucson on the website of the Arizona-Sonora Desert Museum, where you also can take guided tours with a staff expert. This is an outdoor museum, where you sometimes have to give the javelinas and other desert creatures right of way to cross the paths.
Spring is a great time to visit the Sonora Desert -- daytime temperatures are cool and comfortable, and the desert floor is green and pink and purple and red.
Just so you know -- Tucson is 2,389 feet above sea level, and the metro Tucson area covers more than 500 square miles. Arizona does not follow daylight savings time. From April through October, Arizona time mirrors Pacific Daylight Time.