Of the traditional texts, I like the Lial book for self study. It has clear explanations, lots of problems of all types (you don't have to do them all), lots of review problems (again, you don't have to do them all), chapter tests, and cumulative review problems for those who need it. And the solutions manual is excellent. You can get used copies very cheaply online.

If you have a math student who would do well with a discovery approach and extra challenge, you might want to take a look at the Art of Problem Solving series (as arlen1 suggested). They have a book that is called Precalculus, but a student who has finished a traditional Algebra II course might be better placed in their Intermediate Algebra book. They have placement tests to help you decide.