You have a couple of options here. You're essentially trying to annotate your peaks.

1) HOMER has the ability to annotate your peaks to the nearest gene, as well as provides a wide variety of other useful tools. It is a command line tool. The tool accepts HOMER peak files or BED files (specific formatting information can be found on the link). As a generic example the tool would be used in the following way:

annotatePeaks.pl $NARROWPEAK_FILE $REFERENCE_GENOME -gtf $REFERENCE_GTF > $OUTPUT

Where $REFERENCE_GENOME could be one of: hg38, hg19, mm9, etc.

Where $REFERENCE_GTF is a gtf formatted dataset from Gencode, or UCSC.

2) ChIPseeker is a R package available from the Bioconductor 'suite' that can be used for annotation, comparison, and visualization of ChIP-seq data. Your question can be answered via section 5 here. But essentially you'd be using the annotatePeak function.

3) Bedtools is a software suite for genomics analysis tasks. Your question could be answered by using the closest function which searches for overlapping features in file A and file B. If no feature in B overlaps A then it will report the nearest feature in B. This means you'd need access to a BED file that has all your gene coordinates, this can easily be grabbed from the UCSC Table Browser. A generic example would look something like this:

bedtools closest -a $NARROWPEAK_FILE -b $GENE_BED_FILE [any options you might want] > $OUTPUT_FILE

I'm sure there's a variety of other annotation software out there, these are just my commonly used ones, but i'm hoping that others are shared.

You can use BEDOPS closest-features and BEDOPS gtf2bed or gff2bed with a GTF or GFF file containing gene annotations.

For example, to get annotations for hg19:

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

Then run a query:

$ closest-features --closest --delim '\t' --no-ref peaks.bed gencode.v19.genes.bed > answer.bed

The --no-ref option leaves out overlaps between peaks, so that what is reported as nearest is a gene annotation. The --closest option picks the nearest of the two annotations that are upstream and downstream of the peak (depending on strandedness, you may want to leave this out, post-processing with awk or similar to choose based on strand; or add --dist and select based on signed distance).

See --help for other useful options.