Rinse the sushi rice under cold water until the water runs clear. Combine rice and water in a rice cooker and cook according to the rice cooker’s instructions.
In a small saucepan, combine rice vinegar, sugar, and salt. Cook over medium heat until sugar dissolves. Cool to room temperature.
Transfer cooked rice to a large bowl and gently fold in the vinegar mixture. Let the rice cool to room temperature.
Place a sheet of nori on a bamboo sushi mat. Spread a thin layer of rice over the nori, leaving a small margin at the top.
Arrange cucumber, avocado, and crab meat in a line along the bottom of the rice.
Lift the edge of the mat over the filling and roll it tightly. Use the mat to shape and compress the roll. Repeat with remaining ingredients.
Slice each roll into 6-8 pieces and serve with soy sauce, wasabi, and pickled ginger.