If I recall correctly (and it's been over a decade since I read that one), Zinn is quite clear from the onset about his stance. (Even the title makes it evident that his perspective isn't going to follow the traditional USA history narrative.) He sustains his points with empirical evidence, so I would hesitate to call it prejudiced. But there are some issues with some of his sources. (I think Matthew Restall may address some of those.)
How about trying out James Loewen's Lies My Teachers Told Me? That book explains what I think Zinn was attempting to problematize: the blind acceptance of the biases within historical texts. Loewen aims directly at the USA secondary educational system in particular. You will learn a lot about USA history and why it has been written from a specific angle.
John Coltrane's versions of Afro Blue. Very different from Mongo Santamaría's original. I like both approaches, but Coltrane's recordings of it were all just so powerful.