I have a GRanges that represents ~150 genomic regions of interest. I want to use the location of those regions to identify any overlap with gene CDS or Promoters within the yeast genome.

There is a convenient function within the GenomicFeatures package for doing this for CDS.

cdsByOverlaps(TxDb.Scerevisiae.UCSC.sacCer3.sgdGene, MyRegionsGRanges, maxgap = -1L, minoverlap = 0L, type = c("any", "start", "end"), columns = c("txid", "tx_name"))

However, there is no equivalent function for the comparison against Promoters by overlap. There is however, a promoter function that can be run on the TxDb to generate a GRanges of Promoters for the yeast genome.

promoters(transcripts(txdb, columns=columns, use.names=TRUE), upstream=100, downstream=50)

I could then compare my two GRanges (Promoters vs. RegionsofInterest) to find overlap and extract the gene information. I just don't know how to do that within the packages. Maybe I should just shift to base R for this comparison? Any ideas?

The cdsByOverlaps function is really just a convenience function that uses subsetByOverlaps to do what you want. You can do the same thing directly using

prom <- promoters(transcripts(txdb, columns=columns, use.names=TRUE), upstream=100, downstream=50)
olaps <- subsetByOverlaps(prom, MyRegionsGRanges)

Alternatively you could use findOverlaps, which will give you a Hits object that indicates which of the two GRanges are overlapping.