Alfred's Basic Adult Piano Course
I like to use this book for all of my piano students. It is fast paced and doesn't spend too much time on simplistic concepts. Within the first lesson, students are reading music. Through the course of the book students gain the ability top play familiar melodies with both hands. I have had adults and elementary students excel in this book.
Hanon: The Virtuoso Pianist
There is no better book to build finger strength, dexterity, and coordination on the piano. Hanon developed this book to gain better control over the pesky fourth and fifth fingers on each hand (ring and pinky) as well as develop his left (weaker) hand to the ability of his right hand.
These exercises are simple enough to memorize and practice daily, but the key is consistency and evenness within each exercise. Although the music looks intimidating, I have had success teaching elementary students Hanon patterns by rote.