someone 60 years old would have been born in/around 1948, and their teen years would stretch from about 1961 (13) to about 1967 (19). So, assuming that what was popular during these years influenced their tastes heavily, i'm guessing that they might like, among other things, guitar instrumentals a la The Shadows, The Ventures, Dick Dale, Link Wray, The Dakotas, The Surfaris et al. Tom Petty's band recorded an album of surf instrumentals in the 90s as The Blue Stingrays, and the Aqua Velvets are another well-regarded surf revival outfit. psychedelic/garage rock also became popular during this period, and there are lots of bands continuing these traditions too - White Stripes, Black Keys, Comets on Fire, Dead Meadow, Warlocks etc.
EDIT: excuse all the edits - i just got up and i can't type straight yet.