In wordpress you can set an image for each category in Events > Organize.
This image will be used in the widget "upcoming events" in the mouse over preview. Unfortunately the image is not resized on the server. I used a very large a image for a category and the widget on every page. The image made it to the top network-traffic list on my webserver.
Better to create an auto-shrink version of the image on the server when adding it to a category.