Right now, she would need to use the teleport! This is because the other cities are not open to Refugees, and the barriers that keep them hidden would kick her out.

And as for Miyazaki, while there is technically nothing stopping her from flying there, it would be too far away to realistically do so. For an idea of scale, this map shows roughly where Miyazaki is located, keeping in mind that it would take 5 hours by train to go from Tokyo to Osaka!