If you don't need a database, you can get the cost down to around $10-$15/month. Though, I haven't played with their new "Azure Web Sites" option (I use an extra small web role instance), which is apparently free. You can play with the pricing calculator here.
Also note that pricing is very granular (down to the hour). If you only have your website up for an hour in a month, you only pay for that hour.