Haven't used it in a while, but IIRC in the Sources tab of Chrome's Dev Tools, right-clicking a directory brings up a context menu with an "Add folder to workspace" option, which has you pick a local directory to map to the source directory. Then if you edit a file in the dev tools and command-S, it'll save that file where it appears in the local directory you picked.
Not just that, I recently found out that it also auto-saves changes that you make right in the css panel of the DOM inspector. It backs up your original value by commenting it out, but be aware of this when you experiment with this! Fiddling in with css in the inspector will make it persistent!
