Gabrielle
There are a number of devices which might do what you want. A lot depends on how much you want to spend, and also on whether you don't mind wires or cables. For example, you could simply use your computer and appropriate sound card, and drive a suitable amplifier by an SPDIF link. I understand that these can drive up to 10 metres. If your amplifier or other connected input device does not have an SPDIF link, then you might be able to drive another digital or analogue input. You might need to buy a device to connect to the wires/cables for that.
If you don't like wires, then you might try wireless systems. Netgear did one called the MP101, which used MP3 to communicate. Not bad, though some users reported lots of problems. D-Link do a thing which they call Medialounge - see
http://www.dsl-warehouse.co.uk/product.asp?pr=DSM-520 which may also work in a similar way, though it's really geared up to TV usage I think, and you might need to use a TV as a display.
Many people seem to think that Roku products are good. A relatively cheap one is this -
http://www.broadbandstuff.co.uk/product_info.php?products_id=747&gclid=CPrut7_rtYoCFRx6EAodIlboQgThere are several issues of course. One is acquiring the data stream from the Internet, and then theres the business of decoding it and feeding it to your hi-fi and getting decent quality. There's also the business of actually controlling the whole set-up. You don't necessarily want to be continually moving into another room in order to change channels. There are solutions, but a really good solution may come at a price. Some systems do come with a suitable remote control which can control your centralised music distribution point - or maybe even more than one on a network.