I have a set of microRNA binding sites that are listed according to their NM_xxxxx mRNA sequence position. Does anyone know of a tool that would allow me to take these mRNA position values and convert them to the corresponding GRCh37 genomic DNA position values - or in other words the genomic DNA position from which it was transcribed?
This is a clarification rather than an answer. The NM_sequences don't necessarily have a "true" position on GRCh37. They are derived independently of the reference genome, so may or may not map to the genome (and when they do map, they might not map 100%). This means that any means of mapping these NM sequences to the genome is just one possible mapping out of many potential mappings. Also, keep in mind that there are cases where a single NM gene could map to multiple locations on the genome, since the genome has several copies of some genes.
Even if you could get a good mapping from RefSeq (the NM sequences plus some others) to the genome, you would still need to translate your binding site coordinates to their corresponding genome positions. A simple offset might not work if the alignment you're using supported indels. For example, if you have a binding site from positions 10-20 of NM_123, and NM_123 maps to a position on the genome, you might not be able to just "add 9" to the mapping position to find your binding site, because an indel might exist.
If you used some bioinformatics tool to find the binding sites in the first place, it might be easier to run the tool on the genome rather than using the results of running the tool on the RefSeq sequences.