We compute the metrics of the su(2)k1 x su(2)k2/su(2)k1 + k2 and sl(2,R)k1 x sl(2,R)k2/sl(2,R)k1 + k2, characterize their geometry and explore the "duality" k1 half-arrow-right-over-half-arrow-left k2 of the target space. In particular limits of the ratio k1/k2 the latter coset becomes sl(2,R)k x u(1)/u(1) where k is either k1 or k2. This analysis is a starting point for investigating some properties of three-dimensional stringy gravity.