The scaffolding is down at the San Xavier Mission at the moment. Additional restoration work is on hold pending additional fund raising.
Chiricahua N.M. is a 2 1/2 hr drive SE of Tucson. There are nice hiking trails and scenic viewpoints in the "Wonderland of Rocks" that feature excellent landscape opportunities. If you get up early, you can catch the 8:30 am Hiker's Shuttle at the visitor center and take the 4 mile Echo Canyon/Rhyolite Canyon trail down to the visitor center.
The Apache Trail from Apache Junction to Roosevelt Lake Dam is a nice day trip from Tucson offering views of the Salt River, Canyon, Apache, & Roosevelt Lakes; the Superstition Mountains, Tortilla Flats etc.
If you are visiting the Desert Museum anyway, a stop by the Old Tucson movie location may be interesting if you are into Western movies and TV Series. Gates Pass is definitely the place to be for sunsets and moonrises,
Not far from Saguaro NP East is Colossal Cave and about 45 minutes East of Tucson is Kartchner Caverns State Park.
Jim