I tend to look at things and want to fix them to my specs.
An impulse shared by many, many writers -- and not a bad one at all. Shakespeare was known for it. As long as you rework things enough, and bring enough of your own personality and your own particular strengths to your writing, it's a particularly good way to begin.
Since you mention Lloyd Alexander, we can take him as an example: The Prydain books were obviously inspired by the Welsh Mabinogion, there is no mistaking that. But you will not find a character like Fflewddur Fflam or one like Gurgi in the Mabinogion (a Fflam is original!) -- although you will certainly find their names there. And even characters like Gwydion who are closer to their mythical namesakes are not
exactly like them. Dallben is a little like Taliesen, but only in his early history. Orddu, Orwen, and Orgoch -- there are associations with the Fates, and the Triple Goddess, certainly, but I have never seen the like of their individual personalities anywhere else. Alexander took the Mabinogion as his starting point, but from there he went off in many different directions. This is very different from, for instance, what Terry Brooks did in
Sword of Shannara, following Tolkien character for character and incident by incident.
But as for things you might read to expand your horizons: the medieval sources you've already read are an excellent place to begin. If those don't include the Mabinogion, you should probably read that (lots of good material still there that hasn't turned up as a major influence in anyone's work, and you'll have fun picking out the familiar names). LeGuin's Earthsea books, which have already been mentioned in this thread. McKillip's Riddlemaster trilogy -- an interesting and subtle take on magic that permeates the entire book. These books and Earthsea are very good examples of what I meant by taking a single premise and exploring it extensively. The books in the Fantasy Masterworks series give a very broad view of what fantasy can be. Tanith Lee's Flat Earth books (the setting is sometimes reminscent of the Arabian Nights, but not the stories). LeGuin, McKillip, and Lee are also very excellent writers when it comes to style.
A roundabout way to look up some reviews I wrote on some of my favorite fantasy classics:
http://www.sffchronicles.co.uk/forum/11683-some-of-the-books-that-have-inspired-me.html
Then you might find books on the history of magic, alchemy, natural philosophy, and medicine of interest. Books on folklore from around the world. Anthropology, fairy tales. Tolkein, as we know, built his stories around languages, which were his specia area of expertise. You may have some special area of interest that might be applied to fantasy. (McKillip wrote
Song for the Basilisk largely around music. Melanie Rawn, Jennifer Roberson, and Kate Elliott collaborated on
The Golden Key which is built around the art and magic of painting.)
And somewhere around here there is a list I put together of reference books useful in creating the everyday background details that can bring a story to life -- at least if it's something similar to the Medieval period you are interested in. I will pause to look it up ... and here is the link:
http://www.sffchronicles.co.uk/forum/34051-research-novels.html
(Its message #9)