what kind of dinucleotides can be considered important from a mutational point of view other than CpG islands?
In some types of cancers like breast cancer, APOBEC3 cytidine deaminases can become upregulated and enhance mutagenesis. As shown in this mutational signature from cancer tissue data the enzymes prefer TC motifs.

Source: https://cancer.sanger.ac.uk/cosmic/signatures/SBS/index.tt