Which system does she visit first?

Tatooine

The place where she first met her husband so long ago. Tatooine was a barren, desert planet on the outskirts of the Republic. Desert stretching out for miles and miles, all controlled by gangsters and inhabited by wanted men and women.

Recently, shipping lines near Tatooine have been attacked and looted, Chancellor Palpatine suspects that the Hutts were behind it. Padme was secrelty sent to sort it out.