Cool question. Unfortunately, I don't have a complete answer; the best I can do is summarize some literature. I'd be happy to look more if you want to discuss though. Also, sorry the answer is a little scattered and I apologize if you were already aware of all this!
One thing I will suggest though is that this is hard to do for the human genome in isolation; hence why much of the literature draws on other animals as well.
In any case, the literature on this topic is quite expansive, so I am afraid this is merely the tip of the iceberg. Hopefully it's helpful though.
Firstly, I know of two genomic mutation rate maps that might interest you (as you suggest in your question). One in Genome-wide patterns and properties of de novo mutations in humans by Francioli et al, looking at de novo mutations in humans (obviously more concerned with germline mutations), and another in Mutational heterogeneity in cancer and the search for new cancer genes by Lawrence et al, which (unsurprisingly) is concerned with somatic mutation rates and the resulting oncogenics.
A great review, although not entirely human-specific, is Variation in the mutation rate across mammalian genomes by Hodgkinson and Eyre-Walker. They note that:
Small-scale effects: G & C mutate more than A & T, CG dinucleotides are highly correlated to higher mutation in non-coding DNA, and there appear to be hyper-mutable sites (conserved across species) that are susceptible to SNPs. These effects vary across the genome as well. Indeed, certain regions of mitochondrial DNA also have highly variable mutation rates. Oddly, GC-rich islands may be less mutable (for certain mutation types), and may affect nearby nucleotides, particularly methylated ones.
Transciption sites: somatic tissue has lower mutation rates of transcribed areas than non-transcribed ones. In germ tissue, there is an interesting effect for certain types of mutations increasing as one moves away from the transcription start site, but not others.
Other mutations: indel mutations tend to co-occur with point mutations
Mutation rates are spatially correlated at multiple scales.
Chromosomes: for humans, it seems the Y chromosome is the most mutable, followed by the X, and then the autosomes. There is also a difference in the mutation rate between autosomes, but it appears this is overshadowed by the intra-autosomal mutation rates.
Not explicitly noted by the paper, but intutive and sometimes implied, is the lower mutation rate in coding and regulatory regions (e.g. enhancers, promoters,...).
Another paper is Evolution of Local Mutation Rate and Its Determinants by Terekhanova et al. They note local mutation rates in primates (obviously including humans) are highly correlated across the genome. This correlation weakens as evolutionary distance grows (e.g. humans to mice). They also look at the influence of several genomic features on local mutation rates.
Not in humans, but Evidence of non-random mutation rates suggests an evolutionary risk management strategy by Martincorena et al look at mutation rates across E. Coli genomes, finding enormous variability, particularly lower rates in highly expressed genes.
Since we have not yet seen chromatin structure pop up much, I'd like to point out the cool paper The effects of chromatin organization on variation in mutation rates in the genome by Makova and Hardison. Therein, they find that mutations of different types are affected differently by open vs closed chromatin states; roughly, closed chromatin encourages base substitutions, whereas indels occur more often in areas with open chromatin.
Finally, some of the difficulties in assessing mutation variability are explained by Eyre-Walker and Eyre-Walker, in How Much of the Variation in the Mutation Rate Along the Human Genome Can Be Explained?
Some related work
For mutation rates in germ-line cells specifically, see:
which describe some patterns in mutation variability across the genome, but are often more concerned with inter-individual factors.
Also here are two early papers using comparative genomics to look at mutation rates:
which focus on inter-species comparison, but also discuss compositional differences (e.g. GC richness).