Sometimes, you discover the coolest Mac OS X tricks by accident. That happened recently to Hints reader philostein. And philostein's accident is our gain.
First, copy a file path to your Mac's clipboard (by selecting a folder in the Finder and pressing Command-C or selecting File -> Copy). Then, after choosing File -> Save in a new document, press Command-V. That will open a Go to Folder dialog box, with that folder path already pasted into it. When you click on the Go button (or press Return), the Save dialog will navigate directly to that folder.
Surprisingly, the Command-V trick doesn't work in Open dialog boxes--but there is a workaround. From an Open dialog box, press the keyboard shortcut--Command-Shift-G--that, in the Finder, summons the Go to Folder dialog. Then, as before, you can press Command-V, and the copied folder path will again be pasted into the entry box.
If you prefer the mouse, and if you have the destination folder open in the Finder, you don't have to navigate to it again in the Open or Save dialogs. Instead, you can just drag a file from the target folder in the Finder onto the Open or Save dialog box; doing so will instantly open that folder in the dialog. And while we're at it, don't forget that you can get a Quick Look of any file in an Open dialog box by highlighting the file then pressing the spacebar.