Yeah, podcasts in Music went the way of the dodo for iOS6 (or was it even 5). Anyhoo, Downcast is awesome. Doesn't sync with iTunes, but does sync with itself on your other devices via iCloud. So just set it up once on one device and enable iCloud syncing on the others.
+1 on iCatcher.I've heard great things about Downcast, but my personal vote is iCatcher. The developer is constantly responding to feature requests and it keeps getting better every day. Meanwhile, it was already the best podcast app two years ago, in my opinion. It's phenomenal.