I really enjoy Producteev (https://www.40tech.com/2010/09/03/gtd-in-producteev-utilizing-multiple-workspaces/), but it may not be visual enough for you either.
For what you are looking for, keeping in mind the wanting to keep things free, you may want to try going low-tech-ish DIY using a Post It notes style application. If you are a Mac user, you could try Task Card (http://www.taskcardosx.com/), as well.
Another option would be to use Microsoft OneNote. It is a bit of a huge program, but it does allow task creation, project notebooks, and the ability to grab and move/arrange elements as you like, and annotate them as well. One of our readers wrote a guest post on how he uses OneNote here: https://www.40tech.com/2011/03/17/reader-workflow-in-action-gtd-for-freelancers-managing-multiple-projects/
A similar option would be mind mapping programs that allow for tasks, like Mindmanager — you would have to buy that one though.
Hopefully that was helpful!