There are many different methods/packages for doing things like this out there. A little searching will yield many a blog post, Biostars questions, and publications. My usual workflow for this usually goes something like this:
1.) Identify differentially bound beaks.
Assuming you've already called your peaks (with MACS, HOMER, spp, etc), this can be done with software like DiffBind (if you have replicates/many samples) or MAnorm (single samples). They'll derive a consensus peakset and compare it across your control vs treatment conditions. They're also pretty easy to setup and use. This will yield a set of differentially bound peaks.
2.) Identify differentially expressed genes.
It seems most people have tried to move away from alignment-dependent RNA quantification tools (cufflinks2, etc) lately towards inference-based estimation methods (salmon, kallisto) followed by a typical differential gene expression package like DESeq2, edgeR, or limma. These have the advantage of also being much quicker. This will yield a list of differentially expressed genes, which you can then filter/rank by magnitude/p-value.
3.) Identify differentially bound peaks that correlate with differentially expressed genes.
This becomes a little trickier as we don't know your experimental setup, what TF you're ChIPing, or what your control and experimental conditions are. Regardless, I usually take a simple approach first, just looking at the closest differentially expressed genes to my peaks with bedtools' closest or BEDOPS closest-features. This will give you a list with the closest gene to each peak, though it's important to remember that the target gene of a given regulatory element may be up to 1000kb away.
4.) Visualize groups and pathway analyses
Once I have these lists, I try to visualize them across all of my samples to pick out sites/genes that are robust and recurrent. I've grown found of EaSeq for visualizing signal at peaksets quickly in a variety of ways - heatmaps, genome-wide signal profiles, and more. It's also good for looking at individual loci/genes if you're interested in specific examples.
I also usually run my peaks through GREAT, which performs pathway and GO enrichment analyses or genes near your peaks. At a minimum, it usually helps you determine if your results make sense biologically.
This is a rather generic and vague guide, but hopefully it helps you get started.