Contrary to what you may read in the local papers a few weeks from now, there's no historical connection between Easter and Ishtar.
Easter is the modern English name of the pan-Indo-European Dawn Goddess, also known as Ostara, Aušrine, Austra, Aurora, Eos, Ushas, and by many other names. All these names clearly derive from the Proto-Indo-European root for 'east.'
Ishtar is the Akkadian ('Babylonian') name of the pan-Semitic goddess known to the Greeks as Astarte, the Phoenicians as 'Ashtárt, and the Hebrews as 'Ashtóreth (originally 'Ashtéret). The name's original meaning remains unclear.
There's no known historical connection between these goddesses (or, better perhaps, families of goddesses). One is Indo-European, the other Semitic.
The fact that the Indo-European name is clearly derivable from an Indo-European root precludes the possibility that Indo-European speakers could have borrowed her from Semitic cultures. Although the origin of the Semitic name remains unclear, the fact that the goddess was already known among Semitic-speakers before their initial contacts with Indo-European-speaking peoples precludes the possibility of borrowing in the other direction as well.