I usually give to Goodwill because it's close, and easy to donate to. I don't mind if they are 'for profit', because they create local jobs - and they don't mark prices up high. I see many people shop there who cannot afford to go anywhere else, and I am glad that there is a place where someone who hasn't much to spend, can still outfit themselves nicely.
Vietnam of Veterans of America is also a charity I have donated to in the past, they will actually come pick up from your house. They accept the same sort of things GW does - clothing, shoes, small working appliances, home decor, etc. Nothing big like furniture or huge appliances or mattresses.
That being said, how easy is Out of the Closet to donate to? I have to admit, if I have to load up and drive across Atlanta to get to somewhere, I usually will look for someplace closer.