Hi! Newbie here, thought I'd wade into this with my two cents worth. I read The Hobbit and LOTR back in high school, and that was so long ago that Professor Tolkien was still among the living. I can recommend
The Children of Lyr series by Evangeline Walton, her re-telling of the Mabinogion (Welsh legends). This was what I read right after Tolkien, and it's still with me. I also recommend author Caseal Mor's
The Watchers series, which includes
The Raven Game. This is a series of Celtic legends, and the stories told from the POV of one of the characters who is a raven. I read all sorts of books; history, historical mysteries, greek and roman history, and biographies and other stuff. I even read some Tolkien fanfiction! I could also recommend Terry Pratchett, although I consider him a "satirist" rather than a fantasy author. I personally like a good tale that you can step into and get lost in for awhile.