Like others, I'll offer a broad range of fantasy rather assume you want all epic all the time. There will be some violence in these books, but that's neither their reason for being nor their emphasis.
Tea with the Black Dragon by R. A. McAvoy -- charming short novel in which an older woman and an older man, who may be somewhat more than a normal man, try to find the woman's missing daughter.
Midnight Riot (a.k.a.: The Rivers of London) by Ben Aaronovitch -- there is some violence here and a few horrific moments, but this is mainly about a young man finding his place in the London constabulary. His affinity for magic and shrewdness when dealing with magical beings is really more fascinating than those violent moments, and the overall tone of the book is as much comic as dramatic.
The Last Unicorn by Peter Beagle -- another story of a man trying to find his place in the world and the woman who helps him by finding hers. Oh, and there's a unicorn and the unicorn has some issues, too. Like the McAvoy, I'd call this charming, maybe the most charming fantasy I've read.
Druid's Blood by Esther Friesner -- a surprisingly good fantasy pastiche of a Holmes/Watson adventure, though the names were changed I think because Friesner couldn't get permission at the time to use them. Some violence, but not dwelled on.
Bridge of Birds by Barry Hughart -- a lot of readers enjoyed this more than I did, but I did enjoy it and as a loose-footed adventure, it's good fun.
The Stupidest Angel by Christopher Moore -- Moore brings together characters from some of his other novels and they deal with the zombie apocalypse right around Christmas time. Somehow he melds Night of the Living Dead with touches of "The Gift of the Magi" and It's A Wonderful Life and there were moments I had to stop reading so I could stop laughing and breath again. Since I hadn't read the other novels and still enjoyed it, I don't think they are a prerequisite.
Randy M.