I am looking for samples in C# or VB.net that explain how to create a polygon using a X,Y coordinate and creating a buffer around it.
There are a couple ways to do that.
You could use the buffer method of the ITopologicalOperator, which returns a Polygon. That page contains sample code how to do that.
If you want to use a Geoprocessing tool, it's a little more complicated. In one application, I got the X, Y coordinates from a mouse click on the screen and created an in-memory feature class to hold that point. That feature class was the input for the Buffer tool (see this topic as an example). From the buffer tool, I then had the polygon in a feature class.
Retrieving data ...