A good tip for magazines that are current reading material is to store them wherever you tend to do most of your reading. Here, a basket next to the sofa makes them easily accessible, perfect for reading while lounging:
You could follow the same idea and place a basket or rack next to or under your nightstand if you read in bed.
Or near your desk if you tend to do your reading there:
Maybe you have a desk that has built-in storage, like the one shown above right (lucky!). Since chances are you don't, you could consider creating your own storage using display shelves. A magazine wall like this one shown below would be perfect for an office or breakfast nook: