The St Andrews Botanic Garden is 15 acres on the south edge of town, managed by the university, and visited by almost no one who comes to St Andrews for the cathedral and the Old Course. That is a mistake. The garden has a good rock garden, a useful glasshouse range, and a gentle sense of order that makes it the best place in the town to sit quietly.
Entry is free from October to March and a few pounds in summer. The Kinnessburn stream runs through the lower part of the garden. It takes an hour to walk properly and you can easily take two if you're inclined.