Your niece might prefer to have a nice little laptop that she can use anywhere as opposed to a big desktop that's sitting in one place, but hey, that's just me. For $500, you should be able to get a nice laptop that can do handle all the kinds of things kids would do and some light gaming.
Somewhat related, Intel's newer dedicated graphics chipsets are going to make for really good gaming performance on cheaper and thin/light laptops in the future: