I would say they're probably some of the safest areas. Also, AZ is a concealed carry state, so you can carry a handgun without permit as long as you follow the rules and aren't a prohibited possessor. That law makes it a little easier to defend yourself if you would ever need to... not trying to push you towards guns because I don't know how you feel about them, but just know AZ is one of the most gun-pro states so be prepared.
Most of the nicer neighborhoods are pretty good at maintaining neighborhood watch and stuff of that sort, at least with my experience. I was approached by a neighbor who was part of my neighborhood watch and now we are part of it, too. I live in a quiet neighborhood, so it's easy to hear people rustling outside at night or anything of that sort, which hasn't happened to me yet. I lived in the ghetto in west mesa, literally had my neighbor 3 doors down get murdered and stuffed under a bed for 2 months, crazy story... police choppers flying around all night, my place got burglarized and I pulled up right as they ran out my front door - all within one year of living there... but that was a bad neighborhood and you could tell just by how it looks. I definitely learned from that experience and won't live in a place like that again.
those areas you mentioned are some of the nicest in the valley, and I wouldn't be too worried about safety there, but you just have to keep in mind that this is the 5th biggest city in the U.S., so there is bound to be some crime. Based on what your expectations are, I think you will fit in right at home here. O BTW I used to live in Southern Utah, St. George to be exact, and the landscape and weather are very similar. AZ is way better than Utah, in my opinion though.
