There is a fantastic app called Default Folder X – but it's not cheap – around US$35. It enables a plethora of features that you can use in the Open/Save dialog of any app.
On the free side, you could try this trick: when you are in the dialog window for Exporting, you can actually drag a file from the Finder into the Export window, and it will automatically change to that same folder. This at least saves you from having to navigate around in the dialog window, since you are likely to have the window for the folder of the original document already open in Finder.
Finally, just in case you didn't already know, the little pop-up at the top of most Open/Save/Export dialog windows lists your 5 most "Recent Places" at the bottom. So if you used "Open..." to open a file, that folder will likely appear in this list.