The talk shall present chosen aspects of a compact quantum-algebraic description of D-brane geometry in WZW models, extending beyond the semiclassical approximation of the original fuzzy matrix models. It shall be argued that a class of unital algebras - the so-called Reflection Algebras intimately related to Drinfeld--Jimbo algebras - captures certain essential features of stringy geometries, both untwisted and twisted, in compact WZW models and their (simple current) orbifolds, while giving rise to some well-known, and some less so, noncommutative geometries (e.g. Podles sphere, quantum projective plane).