Weather-wise between May and Sept, but take account of times throughout the golfing season (mid-April to mid-October) when the course is particularly busy, impacting on and your chances of getting a tee time. Check busy dates on St Andrews Links Trust website If you are happy to take a chance on the weather, then the shoulder periods of April and October can offer good opportunities. I cover everything here you need to know about how to plan your trip to St Andrews: How to plan a golf trip to St Andrews