Is DNA damage (and lack of repair) what causes aging?
Probably contributes, but aging is complex, and we clearly aren't close to really understanding it. There are regions, for example, called telomeres at the ends of each chromosome that protect the chromosome from degradation. These regions become shorter after each cell division, and this is thought to be one thing that contributes to aging.
It's also important to realize that DNA is also chemically modified - without changing its sequence. This is called epigenetic modification, and is incredibly important. These chemical modifications of DNA, like methylation, are what tell the cell which genes to express in that particular cell. Making stem cells from adult cells is based on altering these chemical modifications of DNA. It's certainly possible that changes in the chemical modifications of DNA contribute to aging.
In the end, nobody gets out alive, and aging is probably programmed into us. Sometimes I agree with the line for My Generation by the Who - ‘hope I die before I get old’..