The edge cases of your scenario and the involved formulas:
three points at distanceInKilometers, slightly less and slightly more
this, for latitudes and longitudes near the maxima, and near the center of your projection (e.g. the date line, the poles). This, for the given center point being near the maxima, and for the points to be found near/over the maxima.
a place where no values are returned
a place where more values are returned than you can reasonably expect in production
others which might depend on your implementation
longitudes and latitudes, possibly distances outside of the legitimate range should be caught by your implementation, but shouldn't require continuous testing.
To compare your results with existing implementations, you can take a look at similar functions in spatial databases (PostGIS, MySQL Spatial, ...) or existing libraries (geos, grass, ...).