Another way to get access to UCSC datasets and do genomic set operations is via the command line, using mysql, wget and BEDOPS tools like gtf2bed and bedmap.

Get all SNP rs* IDs via the command line:

$ mysql --user=genome --host=genome-mysql.cse.ucsc.edu -A -N -e 'SELECT chrom, chromStart, chromEnd, name FROM snp142Common;' hg19 > snp142Common.bed

Get genes and convert to BED:

$ wget -O - ftp://ftp.sanger.ac.uk/pub/gencode/Gencode_human/release_19/gencode.v19.annotation.gtf.gz \
    | gunzip -c \
    | grep -w "gene" \
    | gtf2bed \
    > gencode.v19.genes.bed

Map gene names (in the gene ID field) to SNPs, using bedmap to look for SNPs whose positions overlap those of Gencode genes:

$ bedmap --echo --echo-map-id-uniq snp142Common.bed gencode.v19.genes.bed > snpsWithMappedGeneIds.bed

If you want, you can expand the window around a SNP by some number of bases to allow a looser search ("nearby" genes) by adding the --range option to bedmap.

For example, for a 1 kb window centered on each SNP, add --range 500:

$ bedmap --echo --echo-map-id-uniq --range 500 snp142Common.bed gencode.v19.genes.bed > snp1kbWindowsWithGeneIds.bed