I heartily second Rosemary Sutcliff, although my favorite of her books is actually The Shining Company, which is set a bit later and is based on Y Gododdin.

I loved Renault's The King Must Die and The Bull From the Sea when I was a kid, but I was a weird nerdy child who tried to teach herself to read hieroglyphics (not quite grasping that I would also need to understand ancient Egyptian). So I have no idea whether they'd be too history lesson-y as an adult.