Are there any Philippine based kids' magazines that are appropriate for my 8-year-old niece to read? I don't want her to read anything too "adult" for her age, but still want to encourage her to read.

Yes, there are! You may want to search book sales for Disney Junior Magazine, Disney Princess, K Zone, Total Girl and Sophia the First. If you want more educational ones, buy National Geographic Little Kids or Children's Digest. :)

Mustards Kids Magazine is a good choice too. You may want to start collecting kiddie sections from several Philippine dailies. Philippine Inquirer and Manila Bulletin have their own sections.