I have a Samsung Galaxy S2 running on Android ICS.
I can connect the phone via an audio cable to the stereo in my car and play music through the car audio. I can also pair the phone via Bluetooth to my car for handsfree phone use.

I would like to be able to get rid of the audio cable and use bluetooth for both music playing and handsfree phone use.
Is there an app that can do this? I can't find one.

As far as I know it's simple if your car stereo supports A2DP (The Advanced Audio Distribution Profile). So it's not enough that you can connect via Bluetooth you need the correct profile.

I think there are workarounds but I barely understood A2DP & just got a car stereo with an aux input & SD Card slot.

Yes, any issues would be with the car. I have connected three different Android phones (Orange San Francisco, SE X10 & SE Arc) to my car. I need to press the aux button twice to get it to play.

I can forget this then. My car is a 2008 Honda CRV and they have only recently discovered the iphone for the 2012 models.
It is surprising for a Japanese company that they are so old fashioned with regard to built-in media players.

I use my Galaxy S2 to stream audio to my car audio head unit on a daily basis, via Bluetooth.

Its great for listening to crystal clear Radio 5 Live.

Also acts as a handsfree kit.

I've been using a bluetooth car audio from various android phones for about 3 years. couldn't do without it now, I have a Sony Bluetooth head unit.