Picking a good watermelon can be a challenge. One of the best places to buy a watermelon is at your local farmer's market. These watermelon are picked when ripe, unlike those found in supermarkets. Watermelons sold in grocery stores are often picked early, so they can ripen while being transported. The melons that arrive too early are unripe. Melons that arrive too late are often too ripe and can be mushy.