Magazines and books with furigana
 

I may have asked about this before. But does anyone know of Japanese magazines that are not manga, or books (e.g novels) that have furigana?

Basically children's books will have furigana. Other than that, the only furigana I can recall seeing in books and magazines is only for difficult kanji that not everyone could be expected to know.

Actually, you might want to try the Hiragana Times. It's a Japanese magazine made specifically for Japanese learners. Japanese - English Magazine Published in Japan - About Hiragana Times

I suppose you can subscribe to it. The only time I've encountered it in person was when I was flying back and forth from Japan and saw it in the airport (maybe at Narita and also in San Francisco or LAX).

Novels that have furigana are either childish or classical. The former has furigana so that young children without too much knowledge of Kanji can understand; the latter is because they are difficult to read even for native Japanese.

If you are looking to learn Kanji phrases by studying furigana, I recommend this website to you:
Hiragana Megane (How to Read Japanese)