Hexinator (free, but has paid features.)
One of the few hex editors that actually supports Shift-JIS.
Had to install HxD to remind myself why I don't like it, and that was the reason lol
Otherwise Hex Workshop is pretty nice, since it can highlight different parts of the binary. But it's pretty much abandonware since the last update for it was in 2014.
010 Editor (paid) is okay, but not my cup of tea.
And anyway, the hex editor in Bizhawk isn't meant to be an "all purpose general" hex editor. It's specifically for memory in the emulators, and some regions of memory aren't modifiable by design. Chances are you aren't using it correctly.