It is fairly easy to create a hexbin map using QGIS. This tutorial uses a geocoded database from the GISP…
This article presents a rough idea of how one might mimic a non-contiguous cartogram using QGIS.
Here are a few free online tutorials for learning how to work with and create maps using US Census data.
Iowa State University's Extension and Outreach has over forty GIS TaskSheets available as PDFs for users to access.