Lots of good recommendations here. I'll just leave some +1s for a few I've seen here that I've enjoyed.

Blacktongue Thief: A thief tries to rob the wrong warrior and gets wrapped up in a quest to a distant land besieged by giants. The first of a trilogy, but the ending gives you enough closure to be a standalone read while also setting up where the story will go. Personally, I enjoyed the first-person narration which gives you a colorful look at a somewhat non-conventional fantasy world, although it's still fantasy. If you liked Abercrombie then you might like this. There's a similar focus on flawed characters trying to do the best they can. There is some war and politics but they are firmly in the background and far from the main focus.

Legends and Lattes: A retired adventurer opens up a coffee shop in a land that has never heard of coffee. I'm not sure if "cozy fantasy" was a thing before this book, but it's been held up as an archetypal example. The plot is low-stakes and focuses on the characters and the difficulties of running a small business. Makes a good palate-cleanser between denser reads. No war or politics.

Kings of the Wyld: A retired group of adventurers has to come together for one last job after their leader's daughter ends up trapped in a city besieged by monsters. Admittedly how much you enjoy this one depends on how novel you find the idea of adventuring groups being treated as rock and roll groups. Like literally being a stand-in for rock and roll bands with groupies, managers, and all of that. I've seen some criticism that the book doesn't have much going for it beyond that which is a bit unfair. Following a bunch of middle-aged heroes past their prime was refreshing and I think the author did some interesting things with the main character who only uses a shield in combat and whose main motivation is to make it back to his wife and daughter in one piece. Very little war and politics.

Also, I don't think he's been recommended but you might want to check out Mark Lawrence's Broken Empire trilogy. Admittedly it's not typical high fantasy and it is somewhat heavy on war and politics, but if you liked the grittier, grounded feel of Abercrombie then you might like it. It is arguably darker though and the main character straddles the line between dark anti-hero and outright villain protagonist for at least the first book. But it might be worth checking out if you really liked the First Law trilogy.