Fanmail.biz

c/o TNT
1010 Techwood Drive NW
Atlanta, GA 30318

this is the hq for Turner Entertainment Network which includes: TNT, TCM & TBS (CNN is also under the same corporate umbrella, but they have another address)

Here is a link that includes other TV network addresses (some may not be up to date):
http://www.acb.org/adp/tvnetworks.html

And here is a listing for the TNT network on Yelp of all places which includes their address as well:
http://www.yelp.com/biz/tnt-atlanta

You can always contact a TV show that is currently in production, or an actor that appears on the show in care of the original network it appears on. Some are better at forwarding the fan mail than others though. In some instances it is better to contact the studio or production company responsible for producing the show because most scripted shows are not produced by the networks that they appear on.