Find the diameter of a circle with center (1, 1) that passes through the point (2, -3).

The center of the circle is $(h, k) = (1, 1)$.
The circle passes through the point $(x, y) = (2, -3)$.

The radius $r$ is the distance between the center and the point on the circle. We use the distance formula: $r = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.

The diameter $D$ is twice the radius.

The calculated diameter is $2\sqrt{17}$, which corresponds to option (A).

The final answer is $\text{A}$.