I was born and raised in Scottsdale, Az and just recently moved to Sandpoint last year. I fished all over the state and there are some great places to go. The only places close by in Chandler will be the municipal lakes and the Salt River. The Salt is not too far from chandler, it can be fun to fish but it depends on time of year and the rivers flow. When fishing the Salt go to Granite Reef near the dam, Phon D, and/or Blue Point. Trout and bass can be caught on the Salt. In the summer massive amount of tubers tube that river so get out early or late to avoid them. There is also the dessert lakes that are not too far including Saguaro, Pleasant, Apache, Canyon, and Roosevelt. All great lakes for bass and stripers. Those lakes are all large and I recommend a boat with a decent horsepower outboard to get around them.
If you are willing to travel a couple of hours you can fish the Mogollon Rim, which is not a bad idea to get out of the heat. The rim has 8 lakes and few hundred miles of streams and rivers. The 8 lakes are all stocked but most of them get a lot of pressure. Chevelon is an excellent lake but it is a walk in lake, so there is little pressure. Chevy can be incredible in the Fall and early Spring. Blue Ridge Reservoir is another one of my favorites, its on the opposite side of most the lakes on the Rim but has large browns and bows so it is worth it. You will need some kind of water craft to fish Blue Ridge because there is not many places to fish from the shore.
Some of the best fishing for trout is up in the White Mountains or Pinetop/Showlow area. I believe there are something like 60+ lakes and 650 miles of streams. Some of the lakes and streams in the White Mountains are on the White Mountain Apache Reservation, if you fish on their land you will need a permit. On the reservation they have pay to play lakes as well C&R lakes and everything in between that all can be quality fisheries. The White Mountains is the only place in the world you can catch an Apache trout. Also there is always Lees Ferry near Page, Az. It's a quality fishery that is absolutely beautiful.
There is some great info in some of the previous posts. Cinda at the Orvis shop in Scottsdale is a knowledgeable source of info, she even sold me my first rod and reel. Also check out another forum called
http://www.azflyandtie.com/ for additional info.
Good luck on the move. if you want more detailed info please feel free to PM me.
DC