It can be frustrating to find reading materials at your level when you are just starting to learn the language. Even picture books for children can contain words you don't know because they are meant for parents to read aloud to their children.
Japanese language teachers have begun to follow the example set by English as a Second Language teachers to develop Japanese graded readers. Graded readers follow a set of guidelines to limit the number of words, the grammar, and the length of the text for each level.
One set of graded readers that is commercially available is the レベル別日本語多読ライブラリー. Another set that has been recently developed is called さくら.
In the past two decades, Japanese parents and educators worried about the increasing number of children who don't read for pleasure anymore have initiated a movement called 朝の読書 （あさのどくしょ - reading in the morning） where children are encouraged to read for at least 10 minutes each morning. One of the side effects of the 朝読（あさどく）movement is that a number of publishers have released collections of short stories, essays, and poetry that can be read in under ten minutes in addition to the regular full-length books.
The 10 minute guidelines also works very well for Japanese language learners. Short enough to keep you going and divided up into reading levels, it should be easy to find stories that interest you and will give you just enough of a challenge.
Here are some examples of sets/series that have volumes divided up according to grade.