I have a series of points that each represent a sample taken at various locations across the site. Some points appear to overlap when I display the entire site. Is there a setting to only display one point if overlap occurs? I don't want to disperse the points because I want the positioning to be accurate, rather I would only like to display one symbol if points overlap at the current extent.
As points have no area they can't technically "overlap" unless they have exactly the same XY coordinates. The overlap you are observing is from the marker symbology used to symbolise a point.
More often people want to disperse such data but you are asking to collapse them to a single location based upon a display scale of your site. So do you want to collapse them down to an existing point (if so which one), an averaged location and what distance or "tolerance" are you willing to accept?
So you can see this is not an immediately easy problem to solve and as such there is no option to generalise your data in symbology. What you can do is process your data to generate a new dataset that you would display at your site level scale. Search the Help file for a tool called "Collect Events" and note the usage section about the integrate tool.