We do visit the local library, there are loads of interesting looking picture books but it's much more difficult to decide between those with no illustrations. Our local librarians have, sadly, not proved to be very helpful.
I've found that one way to find something suitable is to sort out one book that you know they've enjoyed and look it up on Amazon. That way you can see other books written by the same author, and suitable books by other authors will be suggested.
f you go the the start page for books on Amazon you can also use the menu down the left-hand side of the page to choose an age, and various subjects (mysteries, humour, fairy stories etc) are offered.
My nine year old granddaughter enjoys non-fiction much more than fiction at the moment and her current favourite book is the Guiness Book of Records! Generally I feel that if anything gets them reading it is a good thing, whatever it is.