Many websites offering Location Based Services (LBS) provide a k NN search interface that returns the top-k nearest-neighbor objects (e.g., nearest restaurants) for a given query location. This paper addresses the problem of crawling all objects efficiently from an LBS website, through the public k NN web search interface it provides. Specifically, we develop crawling algorithm for 2D and higher-dimensional spaces, respectively, and demonstrate through theoretical analysis that the overhead of our algorithms can be bounded by a function of the number of dimensions and the number of crawled objects, regardless of the underlying distributions of the objects. We also extend the algorithms to leverage scenarios where certain auxiliary information about the underlying data distribution, e.g., the population density of an area which is often positively correlated with the density of LBS objects, is available. Extensive experiments on real-world datasets demonstrate the superiority of our algorithms over the state-of-the-art competitors in the literature.