Accurate and up-to-date information about security/safety threats in Israel

The other answer is great, but it addresses only the missiles and indirect fire threat to Israel, posed from Lebanon and the Gaza strip, sadly there are other security threats, the "conventional" terrorist attack, which in the last years took the form of stabbings or vehicle attacks.

For these, there is no preliminary warning system, and there is no "official" measure of how dangerous it's right now to be in certain parts of the country (a system like this exists for travel abroad, where the Israeli foreign ministry will alert Israeli citizens from traveling to certain countries or certain parts of the world because of known threats).

The best source for this is still keeping up with Israeli news. They will not only cover issues that might increase tension in the area (for example, the US decision to move their embassy to Jerusalem) but will also let journalists analyze the situation, many time trying to predict the response from the other side. This holds also for the threat of rockets. They are not fired constantly and are usually fired for a short period of time with something inciting them (not always, and not always predictable). So, if you hear about something that causes increased tensions, you might want to avoid the places more prone to attacks.

Here are three examples for Israeli news sites in English, they are not the only ones:

• Ynet News in English
• The Times of Israel
• The Jerusalem Post