Transcription-factor proteins bind to specific DNA sequences to regulate gene expression in cells. DNA-binding sites are often identified using weight matrices calculated from multiple known binding sites. However, in many cases the number of examples is limited. Here, we report on an atomistic method that starts from an x-ray co-crystal structure of the protein bound to one particular DNA sequence, and infers other binding sites, which are used to construct a weight matrix. The emphasis of the paper is on using the Wang-Landau Monte Carlo algorithm to efficiently sample high-affinity binding sites, which demonstrates that sampling can produce accurate weight matrices in analogy to bioinformatics approaches. For cases of low complexity, we compare to the exhaustive (but slow) dead-end elimination algorithm. To recover crystal binding sites, it is important to include bound water in the protein-DNA interface. Our approach can, in principle, even be applied when no native protein-DNA co-crystal structure is available, only the structure of a closely related homologous protein whose amino-acid sequence is changed to the protein of interest.