I'm only 41 so I can't say for sure, but I think there are plenty of nice, caring 60-somethings out there who would be happy to have a caring lady like yourself. Don't settle for craziness. Put yourself out there so you can be available for someone nice, someone who is wondering where all the good women are.
It's funny, my best friend is a few years younger than me and still in her 30s and she swears there are no good men left out there at our age. Lol! There are nice people available at any age, in my opinion, but everyone's always worried about being alone. The important thing is filling up your life with other things that fulfill you so you will be happy and fulfilled when the right person comes along.