The quadtree is the two-dimensional case of a broader family of space-partitioning data structures. Octrees extend the same idea to three dimensions (splitting cubes into eight children), KD-trees use alternating axis-aligned splits (splitting along x, then y, then x again), and R-trees group nearby objects into bounding rectangles. Each variant makes different tradeoffs between construction time, query speed, and update cost.
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The simplest approach is to check every single point. Compute the distance from the user's location to every restaurant in the database, keep the ones that are close enough, and throw away the rest.
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