Personally, I use doubleTwist for my music files.
As for streaming, you NEED some sort of internet connection to stream music from the internet, and for most tablets, that means Wifi. If you have one with a cellular connection, you better have an unlimited data plan since internet streaming will generally eat your plan at 1MB per minute. Put another way, listening to the radio for 2 hours a day every day will use almost 4GB in addition to any other data you use.
That said, I use TuneIn as it has a selection that Pandora cannot even think of dreaming of… but only on wifi as using it on my data plan even as little as 4 hours a week put me over my 2GB/mth limit.
@Buttonstc Actually, not really. For 3G maybe in areas with spotty reception maybe, but I never had issues in any area where I had at least 3 bars. Catch is, using 3G/4G for streaming murders your data plan (can we say “overage fee”?) while wifi is effectively free.