The Rincon Mountain District of Saguaro National Park is to the east of Tucson. It's significantly bigger and makes up a wide range of distinct lands. From the desert on the edges, to woody mountains in the middle. You can find things in the east that you wouldn't expect in the middle of a desert, such as tall pine trees covered in snow with black bears. Those are all up in the mountains of the Rincon Mountain District.
I stuck to the 8 mile paved Cactus Forest drive, and did some hikes off of it. It wasn't much, but it did offer some incredible sunsets.
The Tucson Mountain district is the smaller of the two parts of Saguaro National Park. It's located to the West of Tucson and contains the main visitor center and a rough loop road. I spent the morning in this section of the park, walking and driving around. One of the nice parts is Signal Mountain, which has ancient petroglyphs.