I attend Meetup groups in my area.. There are hundreds to choose from here as I am in a city. Don't know if you have anything like that. I go to a sketch group once a month. An Italian speaking/learning group occasionally, and have joined an area dance group but not ventured into that. I am thinking instead of the dance group maybe a gym with personal training to tone-up.
I am also 60 and quite introverted. I moved back to my hometown about 3 years ago, and am friendless here but keep contact on FB with family and friends out west. None were close as that is where I falter. I often feel like I am not friend material and don't understand why I feel that way. I study how people interact that are friends, but I miss something I suppose.
The groups help me get out of my regular comfort zone and mindset. I play/practice with them acting different than usual. Like in the sketch group I act very enthusiastic about other peoples art work, and when the group isn't meeting they occasionally post work or links on our online blog place. I answer to all of the posts. It isn't being phony, it is pushing myself to externalize inner questions and comments about things that I otherwise would let ride, and never ask or participate. So when I say play, maybe I mean explore.