The best part of being 60, is that you did all your stupid stuff before the internet.
There are 60 seconds in a minute and 60 minutes in an hour. Gifts like watches and clocks work well, but this could also be used if you want to plan a date with your giftee and spend a few ‘hours’ with them.
High-performance car stats include how fast they can go from 0-60 and a common speed limit is 60 mph. Try working in a car related gift like a road trip or gas cards.
60 is the atomic number for neodymium. It is used in the world’s strongest magnets but could easily fit for a fridge magnet.
Traditional 60th-anniversary gifts include diamonds and irises. These could be incorporated into your theme.