The University has a range of sports and exercise classes, open to members of the public and members of the Sports Centre. For more information please see here: http://www.st-andrews.ac.uk/sport/healthandfitness/programme/
You can’t work in St Andrews and not try golf, can you? 
St Andrews, the ‘home of golf’ boasts seven courses and information about them is here: http://www.standrews.org.uk/
If you’re just starting out, the golfing range can arrange 1:1 or group lessons (sometimes specifically for University staff and students). The golfing academy is a good place to start: http://www.standrewslinksgolfacademy.com/