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There are lots of great non-floral fragrances out there. A great place to start might be some of the unisex or masculine frags. Woody notes might appeal to you. Three of my favorite wood scents are Serge Lutens Chene, Serge Lutens Santal de Mysore, and Tam Dao.
Two non-floral feminine fragrances out of my wardrobe I have to mention are Angel and Eau des Merveilles. Of course, Angel really needs a light hand. Dousing yourself in Angel is not advised!