re: Book recommendations for non-ASOIAF medieval fantasy?

I like many others started out on The Wheel of Time. Epic series but it definitely has many weak points. You might love it but you might also consider a series that is not 14 books long to start with. Game of Thrones might be my No. 3 or 4 so far but here is a rough list of series I have found pleasure in. These are medieval fantasy only in the way that all use swords and other medieval weapons. I think all of them have some amount of magic.

1. Malazan Book of the Fallen - This read is a true epic but it throws you into the deep end and never really lets up. Silmarillion type confusion for the unwary reader. My second read through was undoubtedly my best experience in reading Fantasy.

2. The Kingkiller Chronicle - Unfinished. Great story but it is not done. You know the drill.

3. The Stormlight Archive - Unfinished. Same as above but Sanderson is a writing machine. This is his Opus though so he will take his time on it.

4. The Gentleman Bastards - This is still ongoing but each story is relatively self contained. 3 great books so far with another coming this year I think.

5. First Law Series - Abercrombie has been well represented in this thread and I feel that this might be the closest thing to what you are looking for. I have it at 5 but I love the hell out of this series.

6. The Broken Empire - If you like Abercrombie then seriously give this series a look. I have just completed my first read through and was blown away. Tough, gritty, really just a nice story. I would not say it is complete but the author does not have any plans to continue it at this time. Definitely worth a read.

7. Night Angel - These are fun and quick and I don't think you would regret them. They are about assassins who are trying to save the empire/world.

8. Black Company - This is more of a military history in a fantasy setting. Imagine the Bridgeburners from Malazahn get a whole series to themselves. Not as good of course but well worth the read.

There are a bunch of other great novels and series but I can't think of them now. I would recommend starting with the First Law series like many others have pointed out then going from there.