Rinse rice 3 times. Place in a saucepan and add water; bring to a boil. Reduce heat to medium-low, cover, and simmer until rice is tender and water has been absorbed, 20 to 25 minutes. Remove from the heat and cool to room temperature, 15 to 20 minutes.
Divide ingredients evenly and layer onto 4 plates as follows: rice, crab, cucumber slices, and avocado slices. Drizzle teriyaki over each plate and sprinkle with sesame seeds.