Wilson Mountain trail is a good dayhike, accessible by paved road and great panoramas of the Sedona area.
If you've hiked in southern California deserts Arizona is not too different. Always know your water sources and carry redundant containers. Wear long pants and long sleeves if you can tolerate them - there's lots of scratchy stuff here and bushwhacking can be a pain.
Also, Arizona has a lot of fairly neglected trails and wilderness areas. There's actually a whole ton of protected wilderness areas in this State, but outside of the Canyon, Sedona, and the wildernesses near major towns (basically the Superstitions and the Catalinas), they're largely unknown and lightly visited. This is a wonderful thing if you like solitude, however if you've spent most of your time hiking in well-loved areas like the Sierra, it can take a bit of adjustment. Most trails in this state are in varying states of disrepair. You can't assume just because a trail is on the map that there'll be any sign of it at all on the ground. You'll need to spend more time navigating than you're used to - a GPS is a good idea. You'll need to learn to pick out almost-invisible trails based on vague signs, and separate cow paths from designated trails.