Of
newspapers published locally, the English version of Israel's daily liberal broadsheet
Ha'Aretz comes free with the
Herald Tribune, or you could try the right-wing and rather parochial
Jerusalem Post (not published on Saturdays), good for its Friday entertainment guide if nothing else. The only Palestinian newspaper in English is the weekly
Jerusalem Times, with no international coverage, but handy for giving the Palestinian side of local news stories. Similar in tone and content is the weekly
Palestine Report, and there's a good Israeli
Time/Newsweek -style news magazine called the
Jerusalem Report. The
Jerusalem Times and
Palestine Report are available in East Jerusalem only, since they are boycotted by Israeli distributors. Most British dailies are available in Jerusalem, as are (occasionally)
USA Today and the
New York Times.
You should also have no trouble getting hold of magazines such as Time, Newsweek or The Economist. Eretz, a glossy and rather pricey, but nonetheless fascinating, magazine on the history, geography and archeology of Israel, cannot be bought in most bookshops or newsagents, but is available from SPNI.