My go-to resource for all things Broadway is BroadwayRadio. I've been a longtime listener to their Sunday podcatsts (and Peter Filichia wrote the first theatre book I ever bought for myself). Recently, they've expanded their podcast, so they have one each weekday morning in addition to the one on Sunday. These daily podcasts are shorter (usually around 15 minutes each), and they include review round-ups for shows that have just opened as well as news related to Broadway and the theatre world. The hosts (James Marino and Matt Tamanini) have an obvious love of theatre, and their well-informed and strong opinions are always thoughtful and engaging. Additionally, BroadwayRadio seems to be acquiring new theatre-related shows on a weekly basis, so this is definitely a resource to check out!
Love them or hate them, The New York Times is a wealth of information on Broadway, and their Tony Awards section is extensive, with news, interviews, and videos. I also love following the theatre critics' liveblog and Twitter accounts during the awards telecast.
While this isn't a resource dedicated to theatre, I'd be remiss if I didn't include the interview Broadway producer Scott Rudin did with Terry Gross on Fresh Air. He had some wonderful insights into the backstage world of Broadway. Additionally, if you go into the Fresh Air archives, you can find some excellent interviews with other theatre personalities, including Stephen Sondheim, Sheldon Harnick, and John Kander.
Yes, I know I posted this last year. And yes, I still think it applies.