Spring (March–May) and autumn (September–November) are the best times to visit. Spring brings the plum blossom season (late February to March) on Purple Mountain and the cherry blossoms at Jiming Temple (late March to April). Autumn is mild, clear, and turns the forested hillsides of Purple Mountain gold and red.
Summer (June–August) is hot and extremely humid — Nanjing is one of China's "Four Furnaces," cities notorious for summer heat. Temperatures above 35°C are common and outdoor sightseeing in July and August is demanding. Winter is cold and occasionally snowy; the Massacre Memorial is, if anything, more powerful in the grey cold of winter, but much else is less pleasant.
The National Day Golden Week (first week of October) brings massive domestic tourism crowds throughout China. Avoid if you can, or book well in advance.