The questions you are asking are very broad.
It's still high season here until the end of this month, or some places April 15. I don't know what you mean by "inexpensive" in terms of hotels.
The chain hotels/motels are in perfectly fine parts of town, the hotels in Tempe, Chandler, Scottsdale are all basically fine in terms of safely. Sounds like those internet deals might work out pretty well.
As far as inexpensive food, getting a hotel room with a fridge and a micro will allow you to keep snacks, etc in the room to keep costs down. A lot of the good motel chains, and some other places, have a free breakfast. We have a lot of chain restaurants here, though probably not the same as Ky (we have no Steak and Shake here, for one!

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History? I'll let someone else start in on that... too late in a long day!
Let us know more specifics about what you are looking for and what tourist type activities interest you.