Using the mysql server of the UCSC:

$ mysql --user=genome --host=genome-mysql.cse.ucsc.edu -A -D hg19 -e '
select  distinct
    name,
   chrom,
   txStart,
   txEnd,
   IF(NOT(txEnd < 9933699 OR txStart > 9934385), 0, IF(txStart < 9934385,txStart-9934385,9933699-txEnd)) as distance
  from refGene where chrom="chr1" order by distance limit 20'
+--------------+-------+----------+----------+----------+
| name         | chrom | txStart  | txEnd    | distance |
+--------------+-------+----------+----------+----------+
| NM_001012329 | chr1  |  9908333 |  9970316 |        0 |
| NM_020248    | chr1  |  9908333 |  9970316 |        0 |
| NM_001009566 | chr1  |  9789078 |  9884550 |    49149 |
| NM_014944    | chr1  |  9789078 |  9884550 |    49149 |
| NM_032368    | chr1  |  9989775 | 10002826 |    55390 |
| NM_022787    | chr1  | 10003485 | 10045556 |    69100 |
| NM_052960    | chr1  | 10057254 | 10076078 |   122869 |
| NM_005026    | chr1  |  9711789 |  9789172 |   144527 |
| NM_001105562 | chr1  | 10093040 | 10241296 |   158655 |
| NM_006048    | chr1  | 10093040 | 10241296 |   158655 |
| NR_027045    | chr1  |  9712667 |  9714644 |   219055 |
| NM_001130924 | chr1  |  9648931 |  9674935 |   258764 |
| NM_001010866 | chr1  |  9648931 |  9665020 |   268679 |
| NM_032315    | chr1  |  9599527 |  9642831 |   290868 |
| NM_015074    | chr1  | 10270763 | 10441661 |   336378 |
| NM_183416    | chr1  | 10270763 | 10368655 |   336378 |
| NM_025106    | chr1  |  9352940 |  9429590 |   504109 |
| NM_002631    | chr1  | 10459084 | 10480201 |   524699 |
| NM_198544    | chr1  | 10490158 | 10512060 |   555773 |
| NM_199006    | chr1  | 10490158 | 10512060 |   555773 |
+--------------+-------+----------+----------+----------+

Use bedtools. Download refseq genes from UCSC. Then use bedtools. Have a look at closestBed and intersectBed.

EDIT: Firstly you have to make your input file (chr, coordinates) in bed file.

A simple Table Browser search of these regions do the trick, unless you need something more robust and for larger sets of data (NM_ is the refseq as mentioned above)?

• choose species and assembly
• choose genes and gene prediction
• choose refseq and ref gene
• define regions above
• output format: selected fields (choose at minimum gene name and alternative)

Gives a table delimited text file of gene names. For example, region above chr1:9933699-9934385 (assuming human, hg19) gives (cleaned for display purposes):

name            chrom    txStart    txEnd        name2
NM_020248       chr1     9908333    9970316      CTNNBIP1
NM_001012329    chr1     9908333    9970316      CTNNBIP1

You could use related tables to pull out other IDs and GO terms, etc.

NM_002341 is a RefSeq accession number.

If you want to get a gene official name rather than an accession number, then (assuming these coordinates are on Homo sapiens), you could have a look at this.

A R specific method is the Bioconductor package ChIPpeakAnno.