You can use bedtools closestBed

closestBed 

Summary: For each feature in A, finds the closest 
     feature (upstream or downstream) in B.

Usage:   closestBed [OPTIONS] -a <bed/gff/vcf> -b <bed/gff/vcf>

See also:

How to map a SNP to a gene around +/- 60KB ?

Since noone has mentioned it, you can use BEDTools and python (your cake and eat it too) with pybedtools

With that, the code would be something like:

import sys
from bedtools import BedTool

locs_file = sys.argv[1]
genes_file = sys.argv[2]

for nearest in BedTool(locs_file).closest(genes_file):
    print nearest

Pierre's bedtools approach is probably the best. If you are set on developing you're own in-house application with Python I would recommend using bx.python and IntervalTrees. You can parse a feature list (such as a gene list with coordinates and chromosome) in to IntervalTrees (one per chromosome) and look for the closest intervals to your position(s) of interest. However bedtools will work much quicker and be easier "out-of-the-box".

But learning IntervalTrees can be quite handy for dealing with genomic data in general, especially with Python, so it may be something worth looking in to as a learning exercise.