*** Variety: the International Entertainment Weekly - http://www.variety.com/
“The longest running publication on the business of entertainment in the United States.” While its primary focus is on film and television, it includes information on the business side of theater production and reviews of current theater productions across America.
*** TheaterMania - http://www.theatermania.com/
It started in 1999 and some of its features are comprehensive listings, news, reviews, and interviews.
*** Aisle Say - http://www.aislesay.com/
This website is updated bi-weekly and has theater reviews from 17 different cities if you scroll down the page.