I've often thought that the best way to get access to the richness of Unicode would be a drawing pad, perhaps as part of the keyboard, or as an on-screen area, for use with a mouse. Character maps just seem clumsy to me.

For fun, I tried Eth ð, Thorn þ, and Hungarian ű, all of which it got, but not as the first choice. It did not find the Ing rune, which looks a bit like a < and > combined.