This site hosts a very large number of short stories and other texts, sorted into different categories. These are of course written by native speakers for native speakers, but the reduced length makes the texts more accessible for learners.
Choose a category that catches your interest and start reading! If you find authors you like, see what else they have written. Naturally, difficulty varies a lot between different categories and different authors, so don’t give up before you’ve tried a few different ones if you find it difficult.