Serious question: what is it you read in English for light reading? For reading practice, you want something that you actually want to read, and that is at a level that doesn't frustrate you.
This can mean fiction or non-fiction. Short story collections are a great "in" to modern fiction. (look out for stuff like ショート・ショート = super short stories) People ignore non-fiction a lot which I find peculiar - you don't read non-fiction for fun/relaxation in your native language? Ever? Magazines or blogs or reviews or humorous essays or... anything?
Example from 青空 - while I find a lot of the fiction difficult to get into there, there's a bunch of short non-fiction things by 夢野久作 on there which are quite entertaining, e.g.
書けない探偵小説
Another example - if you want to get into the more classical stuff, look for books/websites aimed at explaining the difficult parts to high schoolers.
Reading manga will not necessarily RUIN YOU FOREVER, either. It's a matter of diet - a bit of junk food is fine, as long as you know it's junk. If you read a range of things, and you can recognise that you probably shouldn't copy the speech patterns of fictional teenagers,
samurai, space pilots, cat people, etc. no problems. Similarly, if you enjoy the stuff on aozora, go ahead - but try not to make that all you read and be aware that some of the vocab/phrasing will be old-fashioned or even offensive.
For those of us who are outside of Japan where physical book acquisition is more of a problem, I recommend haunting ebay and being decidedly unpicky about what you read (I only check genre - I get stuff at under £2 a book and if some of it is not to my taste so be it).
Finally: don't be afraid to quit on things. Sometimes you need to put something to one side and come back when you've got a bit more language experience under your belt. Sometimes that thing everyone keeps recommending to you as the best thing since fried bread just bores you solid. There's plenty of textbooky type stuff you can work on if you want something boring but worthy - reading practice should be at least a little fun.