I bought a few books from the "Japanese Graded Readers" series. If you're not familiar with the series, they are books written in simple Japanese for people in the process of learning the language. The books use kanji for each word, but only use words that the reader will know. (Sometimes stories for children are written only in hiragana, but that's not helpful for an adult who needs to learn kanji) Also, every kanji has furigana. There's no English in the books at all, so you'll have to look up the words you don't know. It's good practice I think. Very realistic.
Each volume comes with five short books. Each book contains one story, or in some cases two or three very short stories. There usually is a moral to the story (appreciate what you have, don't take other people for granted, live your live to the fullest), but it's not pedantic or insulting to your intelligence. There are also some famous stories like Hachikō, or classic stories like Urashima Tarō. There are even stories that present information about daily life, like sushi or kimonos. Each volume also comes with a CD that has audio recordings of all the stories produced using a few good voice actors.
I bought volumes 1-3 from level 1, but there are 5 levels all together (levels 0-4), making 13 books total. If you're trying to figure out your level, I think level 0 is good to start just after finishing learning hiragana. Then level 1 would be like your first year in a language program, level two your second, and so on.
The only problem is that they're kind of expensive at $31 each. I got them from White Rabbit Japan, so there was also the added cost of shipping from Japan to the US. Overall, I think it's a good investment for people who's goal is not just to learn a bunch of random kanji, but who really want to learn how to read Japanese.