May or September

Personally, I only travel in the fall. It's less expensive, less crowded, and not as hot.

No wrong answer. Just about anywhere the northern hemisphere, my answer would be September. My reasoning is the chances of being too cold in May are greater than in September. We were there in September and it was just right. But you might also want to scout out when any major festivals or events are occurring wherever you are going.

Both times are perfectly fine, but in theory September has a slightly greater chance of better weather.

Just there in mid-May. Had a great time. Weather was comfortable.

May has the advantage of longer days, so you'd have more daylight hours for outdoor sightseeing.