If the star is in our galaxy, then you can in principle triangulate your 3d position in the Galaxy from the positions of M31 and the Magellanic clouds.
With access to more specialised equipment (telescopes, spectrographs etc.) it should be possible to identify a set of well-known globular clusters to obtain more accurate Galactic coordinates.
If you have really specialised equipment - like a Gaia satellite (!) - you can use the positions of a network of distant quasars to pinpoint the shift in position from the Sun, using the minute parallax changes due to the differing perspective.
If you weren't too far away from the Sun and had a radio telescope, then the positions of radio pulsars should also give the game away. However, move too far away from the Sun and many pulsars will not be visible because of their narrow beaming angles.
All this assumes you have shifted in space, but not time.