We have a kids toy organizer with storage bins and it works great. I think it beats a toy box as you do not have to keep opening the top and is better than a storage bag because it has a frame and is thin against the wall and stands taller than a bag. Image below is of the one we have.
This one costs about $50 and stands 31 inches high and is 34 inches wide and 11 inches deep with 12 multi colored bins. Organizes small toys, crayons, small books, clothing, etc.