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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The efficiency depends on the query size relative to the data distribution. A small query in a sparse region prunes almost everything. A query that covers the whole space prunes nothing (because every node overlaps), degenerating to a brute-force scan. The quadtree gives you the most benefit when your queries are spatially local, which is exactly the common case for map applications, game physics, and spatial databases.
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