I would like to find an automated way to get the genomic coordinates of the exon flanking a SNP. Are there any programs/websites where you can input a single base coordinate and get out output of the entire flanking exon?
If you have tracks of SNPs and exons, you may use bedtools closest to identify exons flanking the SNPs: http://bedtools.readthedocs.org/en/latest/content/tools/closest.html
You can obtain the track of human gene exons from UCSC Genome Browser http://genome.ucsc.edu or Ensembl Biomart http://www.ensembl.org/biomart/.
If you don't want to use command line, use "Galaxy" at https://usegalaxy.org/. You may find more information at galaxy web page under operates on genomic intervals --> Fetch closest non-overlapping feature. The inputs are same as bedtools.