Perhaps you could tell us what you are interested in? There is at least one noteworthy publication in each field.

For general reading of good, longer pieces I can recommend: New York Review of Books (not only a book review magazine), Foreign Affairs (although I don't agree with their interventionist political stance), The Atlantic (popular with HN readers) and Harper's. I'm sure that you would find something in interesting in each of these, but again, please post what your particular interests are.