Lindsey Davis' Falco books (starting with The Silver Pigs) are mysteries set in Rome (Vespasian's reign). They are heavy on character development, with the history nicely integrated. Although the books are pretty political, they're much less so than, say, I, Claudius - the politics are part of the world. In general, I'd say the history and politics are essential to the books, but not in a way that makes you feel like you're sitting in a classroom.

Falco is a snarky, clever narrator . . . with a lot of bad luck. Also, the love story is A+.

Disclaimer: There are like 20 and I've only read the first couple, so I don't know how they develop.