For robust GPS-vision navigation in urban areas, we propose an Integrity-driven Landmark Attention (ILA) technique via stochastic reachability. Inspired by the cognitive attention in humans, we perform convex optimization to select a subset of landmarks from GPS and vision measurements that maximizes the integrity-driven performance. Given the known measurement error bounds in non-faulty conditions, our ILA follows a unified approach to address multiple measurement faults and works with any off-the-shelf estimator. We analyze measurement deviation to estimate the stochastic reachable set of expected position for each landmark, which is parameterized via probabilistic zonotope (p-Zonotope). We apply set union to formulate a pZonotopic cost that represents the size of position bounds based on landmark inclusion or exclusion. We jointly minimize the p-Zonotopic cost and maximize the number of landmarks via convex relaxation. For an urban dataset, we demonstrate improved localization accuracy and robust predicted system availability for a pre-defined alert limit.