My first suggestions is and will always be: "try joining a martial art dojo/group/team/association". Martial arts range the whole spectrum from strenuous to fairly gentle so it does not matter if you are (or want to become) very fit/competitive or if you just want to relax and improve your general wellbeing and coordination. You can also pick zero-contact stuff like Iaido or Tai-Chi.

Assuming you like the activity (please allow yourself at least three months of constant practice before drawing conclusions) you will almost automatically pick up social contacts through that.