Since you listed the Yokosuka Ombudsman's FB page - just wanted to offer a few more military FB pages.
The NAF Atsugi page (https://www.facebook.com/naf.atsugi) is a good one too, they update it very often. You have to sort through a lot of side conversations that are not relevant for people living off base, but you will get a lot of info in a timely manner. A few days ago, the base was advising its people to stay inside after detecting some higher levels of radiation (those levels are monitored daily on base, and keep in mind, even then the levels were still not threatening to human health), before anyone else was talking about it.
Today, it announced it will be conducting the first wave of evacuations ("the President of the United States has just announced that US military forces in Japan are now authorized to conduct a military-assisted voluntary departure of dependents from Northeast Japan, including the facilities within the Kanto Plain.") The page about the evac is here: https://www.facebook.com/notes/naf-atsugi/voluntary-departure-of-dependents-message-from-the-commanding-officer-of-naf-ats/10150118835184298
Don't panic about the note or other things you see written there. Though it is a reliable source of info, the base will always err on the side of extreme caution. However, the fact that they ARE going forward with a costly and logistically demanding operation of (voluntary) evacuation is big. As ts mentioned, it's not a bad idea to track the advice and info that the US military is being offered.
Another military page with reliable sources of info: https://www.facebook.com/afntokyo