Given a set O of weighted objects, a set S of sites, and a query site s, the bichromatic RNN query computes the influence set of s, or the set of objects in O that consider s as the nearest site among all sites in S. The influence of a site s can be defined as the total weight of its RNNs. This paper addresses the new and interesting problem of finding the top-t most influential sites from S, inside a given spatial region Q. A straightforward approach is to find the sites in Q, and compute the RNNs of every such site. This approach is not efficient for two reasons. First, all sites in Q need to be identified whatsoever, and the number may be large. Second, both the site R-tree and the object R-tree need to be browsed a large number of times. For each site in Q, the R-tree of sites is browsed to identify the influence region - a polygonal region that may contain RNNs, and then the R-tree of objects is browsed to find the RNN set. This paper proposes an algorithm called TopInfluentialSites, which finds the top-t most influential sites by browsing both trees once systematically. Novel pruning techniques are provided, based on a new metric called minExistDNN. There is no need to compute the influence for all sites in Q, or even to visit all sites in Q. Experimental results verify that our proposed method outperforms the straightforward approach.