Yoga is a good physical activity with little sweating and no contact but I don't believe yoga will get you great results by itself. I think yoga is a good complement to many other activities though.
My cousin has taken up boxing as it's a complete sport. He wasn't allowed to fight anybody for seven months.
Squash, a racket sport, is the most popular sport on wall Street. If you get good at squash it will help you socially.
Hipsters are really into rock climbing right now.
Soccer and basketball are the two most popular sports worldwide, both are effective.
If I wasn't injured right now I would do heavy weight training plus HIIT.