A Web design directory need not be a "stand alone" type of directory. I'd look for ranking+quality Web design/discussion/review sites that don't have spammy link-exchange pages but, instead, have some type of quality reviewed mini-directory.
I'm not going to put up a list of such directories but, as forum moderator, I might be open to others listing a few if they aren't junky Adsense overburdened crapola type sites. :P
You can find some lists of directories that might help by searching google for "webmaster directory list" or "high pr web design directory list". You'll have to be pretty specific in the search to find directory lists since "web design" has so many listings.
I usually head on over to DMOZ, drill into my local Geo directory (Like the City/State where you live), and after suggesting my site to DMOZ, I start visiting the competition sites to see where they may be linked from.
If you have a local design company, DMOZ is a quick and painless listing.