Would "quadtree" be the keyword here? That's always the first thing I think of when handling distributed points and doing some (local) measure on them.
Quadtree is one option, and would be my choice for 2D. Most people seem to prefer other structures for various reasons. You may also look at BSP trees, BVH or nested Bounding Boxes. There are others as well.
Related: - Quatree - RTree - BVH - Grid