I found a solution to my own question. It is, I believe, very simple and clean. Based on the amount of scripting and/or installing, it is also very efective as you only have to install it via Install wizard and then run one line.
You can download subinacl here. Although it is officially supported only on Win2k, XP and 2k3, it should work on Vista, 2008 and 7 as well.
Next, you run the following from the command prompt:
subinacl /testmode /noverbose /outputlog=c:\TEXTFILENAME.TXT /subdirectories=directoriesonly X:\*.* /findsid=DOMAIN\username
Where X: is the drive you're scanning and username is the user whose permissions you'd like to list. Scanning can take some time and you get the results in TEXTFILENAME.TXT.
If you use the switch /noverbose you get a compact list of access permissions - basically you see which directories the user has access to (with access masks and some other stuff that might come in handy sometimes).
I used OpenOffice Calc to import the list and then applied a Custom Filter and filtered only for those lines starting with +FILE. This lines contain directories the user has access to. This is how using simple tools you end up with only relevant information.
Since inheritance is often enabled on parent directories the actual number of directories you might need to visit to adjust permissions is usually significantly lower than the list itself.