My favorite site for news in Hebrew is Walla.  The Hebrew site is at: http://www.walla.co.il/ .  They have pretty good radio stations too – if you want to listen to music in Hebrew but make your selections from an English menu go here: http://radio.walla.co.il/ts.cgi?tsscript=index.english&fg=1

This site is a terrific news site for Israel, they offer an English version and a Hebrew version.  http://www.ynetnews.com/ and http://www.ynet.co.il/ Its great practice to read the Hebrew version, and then flip over to the English when you don’t understand something.  The company has a great product too called the Megaphone run by Collactive at this address: http://my.ynet.co.il/collative/  The idea behind the Megaphone is that you get desktop delivery of hot news, and a way to proactively respond to legislators, etc. about the news.  Its a really powerful community tool.