At present, no locally produced English TV is in the morning. Cable and satellite TV give much more English programming. Modest hotels rarely have bilingual sets. However, the other papers have their advantages too. All local papers give TV listings which identify those few programs available in English.
Japanese newspapers take periodic holidays when only the sports tabloids are available.
The International Herald Trib and USA Today are available at an amazingly high prices and are hard to find but may be worth it if you want to know what's really happening in the rest of the world. The Tokyo Journal is a monthly magazine with lots of useful information, ads and announcements for foreigners, and stories about the Tokyo area. TJ now has some giveaway competitors with ads and current event information and these can be found at bars in Roppongi and groceries catering for foreigners such as National Azabu in Hiroo. Foreign magazines are very expensive. Kunikuniya and Jena have wide selections.