I often get the query "what is a good website for astronomy?". My instant answer is "Astronomy Picture of the Day". If you're only going to check one site, choose this. One picture plus a paragraph of text each day, that's it-- simple, elegant, informative, beautiful.
If APOD piques your interest, there are good sites to go deeper. "Imagine the Universe" is a useful resource site. Don't let that Imagine lists as 'for age 14 or older' dissuade you. It's a great "facts" site, especially the "Ask an Astrophysicist" section-- full of common questions and answers delivered at a 'high layman level'. Matter of fact, years ago I contributed some of the answers.
For my current field of Sun-Earth stuff, visit SpaceWeather.com. For topical astronomy, Universe Today is an nice current-astronomy-news site, sharing forums with the same astronomer that runs the BadAstronomy blog (that debunks myths and movie-isms). I find it easier to read and more relevant than the usual corporate or government sites, with less bias than most.
You can also customize your home page or iGoogle home to include feeds from Universe Today, New Scientist, Science @ NASA, ScienceDaily Headlines, SPACE.com, and others to get a once-a-day look at current science & space news. I do that just so I can know what is going on outside of my field.
If you like podcasts, there's Slacker Astronomy. They are group of post-docs who do a regular podcast on a current topic, and their motto is "Because if you aren't going to care about something, may as well not care about astronomy." I confess I sometimes miss their latest podcast, but I really, really like their motto.
Finally, I recommend ScientificBlogging.com, especially this one column called "The Sky By Day" by someone dubbing himself the Daytime Astronomer. If you visit and comment often enough, this column gets promoted. And I so want to be a 3rd level blogger.