Easy to read " real " newspaper?
No Problem. Just klick below:
http://asagaku.com/
However, I would recommend asagaku.com first, only after passing N3 or you will just be spending the whole day looking those grammar and Kanji's up which can be very very frustrating. The newspaper itself are intended for Japanese students so you can expect it to be at a very high level. First try,
朝日小学生新聞 『毎日発行』 (No explanations needed here, just read it)
- 1006字 「1年ー6年」 (Kanji's expected from Japanese students)
afterwards, you can try
朝日中学生新聞 『毎週日曜日発行』
- 1945字 「中学」
(Actually, you can just go to the website and help yourself. I'm not going to explain everything here. If your Japanese is between N3 and N2, you should be able to navigate yourself freely and understand almost everything.)