We just returned from a great 9 day trip to southern Utah and are planning on returning the middle of September. The weather should be awesome and most of the kids will be back in school but...
The weather in this area can change in a heartbeat so you will need to monitor conditions closely. With the internet and smartphones this is very easy to do. When we drove to Moab the weather was great but 2 hours behind us a blizzard dropped down onto Monticello {7,200'}, and the Lasal Mountains closing the pass over to Colorado.
Plan on a wide range of conditions, pack and dress accordingly and you will have a blast. Do not miss Capitol Reef NP, even more spectacular than Arches and Canyonlands. Assume Bryce Canyon will be cold as it often is and Zion is just about perfect in September. The north Rim often shuts down early as, like Bryce, it sits at around 9,000'. The South Rim is milder but far more crowded.
:B