I also recommend the Brother CS6000i. I recently gave mine to my niece and nephew (ages 8 & 11) and it's a great machine for people that age. It has lots of modern features like drop-in bobbin, clip-on feet and needle up/down buttons so it's easy to use. Lightweight. Easy to thread. Uses common bobbins. And I don't know about your granddaughter but my niece & nephew LOVE the decorative stitches that it comes with.
They love that thing. Best gift I ever gave them!