Wha? Before the Eastern Temple and/or Tower of Hera?
I've been exploring the overworld, committed to doing some other dungeon before the two I'm being told to do (Hera and the windmill). Doesn't seem to be possible, though. There must be something I'm missing. Can someone just say 'There's something you're missing' and I'll keep at it, but as of now I'm about to give up and just follow the linear path.
Well, no. You have to do Eastern first, and then you have the choice of Hera/windmill. After that, you have the choice of 6, since one of them is a prerequisite for another.