Other than the big media outlets in Israel, like Haaretz or i24news, broadcasting from Jaffa Port, there are a couple of places where you can stay updated with what’s going on in Tel Aviv.
TimeOut Israel has loads of information for tourists, from accommodation to culture and night life, and most things in between. Check it out especially if you’re planning to leave Tel Aviv and want to see what’s going on in the rest of the country. Other than online, you can find a printed version, mostly in big book stores around the city or in tourist information centres.
Apart from that, Tel Aviv has its own English-language radio station, TLV1, with shows about a variety of topics concerning life in Tel Aviv, its history, music, Israeli politics, and even some basic Hebrew words you should know.