Check out TuneIn
Do a search for "radio" in the app store and you'll find a raft of them. The one I like is TuneIn, which has most of my local radio stations- all of those that also broadcast over the web. Of course, you'll use some data when listening to any of these apps, but the sound will be near-CD quality without the reception problems of listening through an FM tuner. TuneIn also has my local AM stations. If you find a station you really like in another city, you can listen to it just as easily. Also, you can listen by genres (news, talk, sports, etc.)
This is as close as you're going to get to an FM tuner for your iPhone without a third-party add-on device.