Unlike many suggestions like Eriskson and Bakker, this series is low on magic.

Instead, it is heavily character driven. Major plot points are not "X can do Y piece of cool magic". Magic exists, though it is very low key. It is well integrated into the story, and most importantly, the character of the person attempting to wield it is critical.

Certain archetypes like "secret, unwanted son of major noble" are taken to logical conclusions.

But most critically (for you), the story is not epic fantasy. There's no Dark Lord. There is no Evil. There are hardly any bad guys. Conflict is driven by differences in perspective between believable human characters, and many times, both sides are shown as rational. Which makes the story seem very real, for all that it is a fantasy.

Also, the series is complete, and comes with some really excellent cover art to boot.

Also, Abraham has collaborated with Martin (IIRC), and Martin has strongly endorsed his series.

Incidentally, the series is called the Long Price Quartet.