There is a browsing collection on the 22nd floor of the W.E.B. Du Bois Library that has been carefully curated to provide a range of reading materials for people who are building up their Japanese reading muscles.
Graded readers are often the first recommended step for people who want to read outside their textbook. Graded readers use strictly controlled vocabulary and grammar. The intent is that students will be able to read 97% of the text without looking up any words and that the unknown words will be comprehensible based on illustrations and context.
It took many years for there to be a reasonable good selection of Japanese graded readers, but the situation is looking better and better. The leader in this field is definitely NPO Tadoku who offer commercial graded readers complete with audio tracks. They are available in print or as e-books.
One of the benefits of many Japanese programs starting to offer Japanese extensive reading classes is that the classes are creating their own graded readers and sharing them freely over the web. One place to see the offerings, especially through the instructors connected to NPO Tadoku is on the Tadoku website here.