You could use BEDOPS bedmap to map your sorted intervals against a BED data stream or file containing gene annotations (e.g., GENCODE):

$ wget -qO- ftp://ftp.sanger.ac.uk//pub/gencode/Gencode_human/release_18/gencode.v18.annotation.gtf.gz \
    | gunzip --stdout - \
    | gtf2bed - \
    | bedmap --echo --echo-map intervals.bed -​ \
    > answer.bed

You could filter this answer for subcategories of GENCODE annotations using grep, e.g.:

$ grep -i "utr" answer.bed > utr.bed

To run command-line tools in R, you can use system().

Have you looked at biomaRt?

Option 1: GenGen (You can use exact overlap OR plus/minus x kb)

http://www.openbioinformatics.org/gengen/tutorial_scan_region.html

Option 2: Homer (This helps in identifying the nearby genes to the given genomic intervals)

http://homer.salk.edu/homer/ngs/annotation.html

Command: annotatePeaks.pl input.bed PATH_TO_GENOME/hg19.fa -gtf PATH_TO_GTF/ensembl.gtf > outputfile_annotated.txt

This should be the easiest way using just an GTF (Example: Ensembl GRCh37) annotation file and genome file (Example: hg19).

GTF: ftp://ftp.ensembl.org/pub/release-74/gtf/homo_sapiens/

Genome: http://hgdownload.cse.ucsc.edu/goldenPath/hg19/bigZips/hg19.2bit