Random point generator

I would like to generate a Random point on the X-Y Plane within a boundary curve using RhinoCommon.

What is the best way to generate it without doing too many tests on whether the point is in the boundary?

Depending on the shape of the boundary curve, you could determine its bounding box (i.e. rectangle) and put a random point inside the box (random widht/height). Then, test inside/outside with one of the Curve.Contains(...) methods. The curve must be closed of course.