Fortunately, some Japanese newspapers do release children's versions, such as the Yomiuri Shimbun and NHK News. This is great for practicing your kanji and increasing your vocabulary.
1. NHK News Web Easy
This one has furigana all over. Some people don't like it, but I do. I can read the kanji that I know without looking at the furigana, and then I just check the furigana after I finish guessing the reading. Also, the articles here are more recent. Best of all, this has AUDIO, so you also get to practice your listening skills as well!
2. Yomiuri Shimbun