First, full disclosure, I can't speak Icelandic. Ég tala ekki íslensku. I am just an old computer guy who has been trying to learn for many years, and still makes weak attempts now and then. So, of course, take anything I say with a grain of salt, as I probably have no idea what I'm talking about.
visir.is - this is a web portal vísir means "indicator" and is sort of an icelandic yahoo.
Go there and click on útvarp (meaning "radio" - literally "out-cast" as in "broadcast".) Icelandic is very cool that way, not borrowing words like "radio" but making up their own.
Anyway, click on that link and you will get a list of radio stations. I recommend the last one "apparatið", it seems to play more Icelandic music, less English language pop. These are mainly music stations. For talk radio see RUV below.
RUV is the Icelandic National Broadcasting Service, much like BBC or Canada's CBC. They have two audio streams RAS 1 and 2. These are great to hear spoken Icelandic.
Want to see what Icelanders read for their news and see how well you're doing or how far you have to go? Here is Iceland's largest newspaper's web site. Don't get too frustrated if you have a hard time reading anything here. news sites tend to be a bit more difficult, in my opinion. They tend to use compuond words more than everyday speach.
TV and movies
I am currently watching The Lava Field (Icelandic title: Hraunið) on Netflix in the US. It seems like Iceland is jumping on the nordic noir train with this, but it's great dialogue that I can sometimes follow!