Embodied intelligence fundamentally requires a capability to determine where to act in 3D space. We formalize this requirement as embodied localization -- the problem of predicting executable 3D points conditioned on visual observations and language instructions. We instantiate embodied localization with two complementary target types: touchable points, surface-grounded 3D points enabling direct physical interaction, and air points, free-space 3D points specifying placement and navigation goals, directional constraints, or geometric relations. Embodied localization is inherently a problem of embodied 3D spatial reasoning -- yet most existing vision-language systems rely predominantly on RGB inputs, necessitating implicit geometric reconstruction that limits cross-scene generalization, despite the widespread adoption of RGB-D sensors in robotics. To address this gap, we propose SpatialPoint, a spatial-aware vision-language framework with careful design that integrates structured depth into a vision-language model (VLM) and generates camera-frame 3D coordinates. We construct a 2.6M-sample RGB-D dataset covering both touchable and air points QA pairs for training and evaluation. Extensive experiments demonstrate that incorporating depth into VLMs significantly improves embodied localization performance. We further validate SpatialPoint through real-robot deployment across three representative tasks: language-guided robotic arm grasping at specified locations, object placement to target destinations, and mobile robot navigation to goal positions.