As ever with Spatial Indexing, you end up finding that testing a variety of grid settings on your data set can yield different results to those of others. That said, I find setting Low at all levels, or Medium, Low, Low, Low yields great results with Points due their simplistic nature.
To make best use of the index however, consider optionally buffering the point and checking for an intersection. Again, I've found it often yields better consistently low result times but test it on your data.
DECLARE @point GEOGRAPHY = GEOGRAPHY::STPointFromText('POINT(<coords>)', 4326);
DECLARE @radius INT = 1000;
SELECT
*
FROM <table>
WHERE <GeographyColumn>.STIntersects(@point.STBuffer(@radius)) = 1;
Try to stay away from the urge to switch to Geometry, as whilst it'll yield ever-so-slightly faster queries, it has more chance to yield "incorrect" results due to working with a planar model. That said if the search distances are small enough, the difference will not be noticeable in most scenarios.