I found that I could keep a copy in the place where I usually would and sync with the cloud by creating symbolic links to the folders that I want to sync inside the Dropbox folder. Using this method, the file would be available in both places, without taking up any extra disk space.
To do this, you need to use the Terminal. Since Dropbox allows you to choose where your Dropbox folder resides, there's no "one size fits all" solution, but here's the general syntax (replace username, foldername, and path/to/dropbox with your own values):
ln -s /Users/username/Documents/foldername /Users/path/to/dropbox/Files/
You can also drag the source and destination folders into the Terminal window instead of typing the paths. Note that foldername has no trailing slash (/), but that Files/ bit does -- this is very important!
With symbolic links in place, you can save files where you normally would, and they'll still automatically sync to the cloud.