Prepare the sushi rice according to the package instructions. In a small bowl, stir together the rice vinegar, sugar, and salt. Pour the mixture over the rice and stir to coat it. Let it cool and refrigerate overnight.
To make each piece, place a 2 1/4-inch circle of smoked salmon in the center of a square of plastic wrap.
With clean hands, mold 1 3/4 tbsp. of prepared rice into a round shape. Set it on top of the salmon.
Gather the plastic wrap and twist it tightly, compressing the filling into a neat ball. Unwrap it and set the ball, salmon side up, on a platter. Cut features from nori and set them in place (tweezers are handy for this).
Repeat the above steps, but substitute a thin slice of avocado for the salmon and form the rice into an oblong shape instead of a round one (twist the wrap gently to shape the avocado without squishing it).