Please help me get in touch with playwright/director David Mamet.  I
want to recommend a gifted actor for his upcoming projects.  Thank
you.

I suggest sending a letter to David Mamet through his agent:

William Morris Agency 
151 El Camino Dr. 
Beverly Hills, CA 90212, USA 
 
Tel.: (310) 859-4000 
Fax.: (310) 859-4462
 
http://www.filmmakers.com/artists/mamet/biography/

Here's another possibility. David Mamet's play "Romance" is currently
under production at Atlantic Theater Company (Mamet was a co-founder
of this theater company). I would think it likely that a letter to
Mamet sent to the theater's address would reach its target.

Atlantic Theater Company
336 West 20th Street
New York, NY 10011
(212) 645-8015
(212) 645-8755 fax

http://www.atlantictheater.org/2004/2004address_phone.htm

My friend and colleague googlenut has passed along some information
that you may find helpful. The Directors Guild (www.dga.org) lists
Mamet's agent as:

JOHN BURNHAM 
INTL CREATIVE MGMT INC 
8942 WILSHIRE BLVD. 
BEVERLY HILLS CA 90211 
(310) 550-4000

According to IMDB Pro, this is David Mamet's current contact info:

International Creative Management 
8942 Wilshire Blvd.
Beverly Hills, CA 90211-1934 USA  
Tel: 310-550-4000  Fax: 310-550-4055 
Web: http://www.icmtalent.com/  

Please let me know if any of these suggestions pay off.