You can do this using Ensembl BioMart (using the Ensembl API is another option), http://www.ensembl.org/biomart/martview here is the XML representation;
<Dataset name = "hsapiens_snp" interface = "default" >
<Filter name = "consequence_type" value = "3PRIME_UTR,3PRIME_UTR&NMD_TRANSCRIPT,5PRIME_UTR,5PRIME_UTR&NMD_TRANSCRIPT,COMPLEX_INDEL,COMPLEX_INDEL&NMD_TRANSCRIPT,COMPLEX_INDEL&SPLICE_SITE,ESSENTIAL_SPLICE_SITE&INTRONIC,ESSENTIAL_SPLICE_SITE&INTRONIC&NMD_TRANSCRIPT,FRAMESHIFT_CODING,FRAMESHIFT_CODING&NMD_TRANSCRIPT,FRAMESHIFT_CODING&SPLICE_SITE,FRAMESHIFT_CODING&SPLICE_SITE&NMD_TRANSCRIPT,HGMD_MUTATION,INTRONIC&NMD_TRANSCRIPT,NON_SYNONYMOUS_CODING,NON_SYNONYMOUS_CODING&NMD_TRANSCRIPT,NON_SYNONYMOUS_CODING&SPLICE_SITE,NON_SYNONYMOUS_CODING&SPLICE_SITE&NMD_TRANSCRIPT,PARTIAL_CODON,SPLICE_SITE&3PRIME_UTR,SPLICE_SITE&3PRIME_UTR&NMD_TRANSCRIPT,SPLICE_SITE&5PRIME_UTR,SPLICE_SITE&5PRIME_UTR&NMD_TRANSCRIPT,SPLICE_SITE&INTRONIC,SPLICE_SITE&INTRONIC&NMD_TRANSCRIPT,SPLICE_SITE&SYNONYMOUS_CODING,SPLICE_SITE&SYNONYMOUS_CODING&NMD_TRANSCRIPT,STOP_GAINED,STOP_GAINED&FRAMESHIFT_CODING,STOP_GAINED&FRAMESHIFT_CODING&NMD_TRANSCRIPT,STOP_GAINED&NMD_TRANSCRIPT,STOP_GAINED&SPLICE_SITE,STOP_GAINED&SPLICE_SITE&NMD_TRANSCRIPT,STOP_LOST,STOP_LOST&NMD_TRANSCRIPT,STOP_LOST&SPLICE_SITE,STOP_LOST&SPLICE_SITE&NMD_TRANSCRIPT,SYNONYMOUS_CODING,SYNONYMOUS_CODING&NMD_TRANSCRIPT,WITHIN_MATURE_miRNA,WITHIN_NON_CODING_GENE"/>
<Attribute name = "refsnp_id" />
<Attribute name = "chr_name" />
<Attribute name = "chrom_start" />
<Attribute name = "consequence_type_tv" />
<Attribute name = "ensembl_transcript_stable_id" />
</Dataset>
<Dataset name = "hsapiens_gene_ensembl" interface = "default" >
<Filter name = "hgnc_symbol" value = "SPTA1,THRB,PDGFRA,KIT,LRRC16A,SCGN"/>
<Attribute name = "hgnc_symbol" />
</Dataset>
The answers below give solutions using UCSC. However, UCSC uses dbSNP131 only, while the 1000g has put many more in dbSNP132. If it were me, I would try to use dbSNP132.
Thanks a lot @lh3.