A "natural zoo" where you can learn about all kinds of desert wildlife and plants. You will see more animal activity if you go in the morning while it is still cool out. Geographically close to Saguaro National Park West and Old Tucson if you're looking to stack things for time efficiency.
Catalina State Park is the closest hiking area to the wedding venue and hotels. And also, where we got engaged! I recommend using AllTrails to review the trail options. Birding Trail and Nature Trail are short loop trails that are good for people across a wide range of ability levels and ages. More seasoned adventurers can pursue Romero Pools or 50-Year.
Mt. Lemmon is worth taking time to drive up. There is a guided audio tour available for both Apple and Android phones. Search "Mount Lemmon GPS Audio Tour" in your app store. Or you can drive up at your own pace and stop at the lookouts to take in the views. There are hiking trails and campsites along the mountain. And a "town" called Summerhaven at the top where you can stop by the general store for a souvenir and the Cookie Cabin for a snack. The base of Mt. Lemmon is about a 40-45 min drive from the wedding venue and hotels. We recommend Le Buzz on Tanque Verde if you're looking for coffee, breakfast, or lunch while near Lemmon.
Note, there are two parts of Saguaro National Park on opposite sides of town distinguished by West and East after the name. We are closer to the West park which is why it is the one that we mention. Both are great. The East park is, as the name indicates, in East Tucson and out closer to Mt. Lemmon.