I agree strongly with the Gaiman and McKinley recommendations. As well as Pullman.
If you like urban fantasy, Jim Butcher (Dresden Files), Patricia Briggs (Mercy Thompson books), and Charlaine Harris (Southern Vampire novels) do nice jobs with it. Also, Sunshine by Robin McKinley is fantastic. Amazing. Lovely.
Still in urban fantasy, I’d also recommend American Gods and Anansi Boys by Neil Gaiman and Good Omens by Neil Gaiman and Terry Pratchett. At the risk of getting too far into vampire fiction, there is also The Historian by Elizabeth Kostova (you should probably not hate history for this one—much of it reads like an incredibly enjoyable history book. Granted before reading it, I would not have said those really exist, but that is how it reads).
For some Victorian fantasy fiction, you can pick up Jonathon Strange and Mr Norrell.
For some great short stories, there are several collections by Neil Gaiman in a variety of settings (Smoke and Mirrors, Fragile Things, M is for Magic) or the Ladies of Grace Adieu and Other Stories by Susanna Clarkson (author of Jonathon Strange and Mr Norrell). I would also highly, highly recommend Ray Bradbury. He’s sometimes sci-fi, sometimes fantasy but also well written. I’d start with the Illustrated Man.
If you want more fantasy world fantasy, Robin McKinley still does great stuff. She has a mini series—which is really to say that she often writes in the same fantasy world, so you will find small pleasures in later books if you start with The Blue Sword and the Hero and the Crown. They are directly related, but later books only very lightly reference them.
I’ve always felt that Hitchhiker’s Guide is a good bridge between fantasy and sci-fi. If you enjoy that, there is also Starship Titanic. I do not recommend his other series the Dirk Gently books. Not at all.
If you don’t mind YA, Tamora Pierce is a fantastic author. You should start with the Lioness Quartet—they were her first books and in that world, all of her books build the world up chronologically. So you can start with just about any quartet, but you’ll get the most enjoyment from starting at the beginning. For the Circle world (her other series), you need to start at the beginning, but just power through the first book. They get better. (I actually quite like the first one now, but at the time, not so much.)
Lastly, Patricia C Wrede is a great author. The Enchanted Forest Chronicles are fun, quick reads. She’s also coming out with a new series that starts with the Thirteenth Child that is just great. I think it is YA, but all of my friends read it in Chicago when our librarian friend got an early copy. There was actually an in-house waitlist.