I had an idea of using a map of Minnesota, with a tree superimposed on top of it. My state has an irregular border–instantly recognizable if you know anything about American geography. Also tree shapes can be pretty complex, and I wanted some roots on the tree. That ruled out using raster graphics, since the logo would probably get pixelated and look even worse. To find the graphics I wanted, I searched Google for Scalable Vector Graphics (SVG), an open standard for vector graphics files.
Google image search has the option, under Advanced Search, to filter results by Usage Rights. I set it to only return images under Creative Commons licenses or in the public domain. (You can do a similar search on Flickr.) I found a suitable SVG file with the Minnesota shape on Wikipedia, although it had lots of extra graphics I didn't want. I also found a good tree graphic, with roots even, except it had some grass I didn't like.
To edit SVG files, there are myriad choices of software from commercial vendors, like Adobe Illustrator. But that would set you back a few hundred dollars! Instead, I used a free application, called Inkscape, that works just as well. You can download Inkscape for Windows, MacOS X, or Linux.
I isolated the shape of Minnesota from the surrounding map, changed the color, and added a thin border. If you've used any other vector graphics software, Inkscape works about the same way.
Next, I got rid of the grass in the tree drawing, and pasted it on top of the Minnesota map. Then it was just a matter of resizing and aligning them until I was satisfied with the result. I know it's still ugly, but lots of people with actual talent use the same tools, and create great looking graphics. Your mileage may vary.