Is it possible to figure out your location in the Milky Way if you are suddenly wormholed to a random, distant location in the galaxy? If you were flying along in your spacecraft somewhere in our solar system and then a large, stable wormhole suddenly opened and you flew into it and were whisked away to some distant location in the galaxy, would you be able to figure out where you were? 

Obviously, a large stable wormhole is exceedingly unlikely, and then there's the matter of the power of your onboard computer and telescope(s). But all that aside, I'm wondering if it would be even theoretically possible to figure out where you were, since the constellations would probably be unrecognizable and you wouldn't have an understandable flight path.
Assuming you had access to the relevant astronomical catalogues and data, then yes it would.

Looking at constellations would of course be hopeless and most stellar catalogues only contain star positions for a relatively small volume in our Galaxy. However, there are classes of object inside and outside the Galaxy that would do the job.

A displacement in our own Galaxy would produce a notable displacement in the positions of local group galaxies, like Andromeda and M33, with respect to distant quasars that define the ICRS coordinate reference frame.

Providing one had the means (i.e. telescopes) to make the necessary observations, then it should be relatively straightforward to reconstruct your position in the Galaxy from the new apparent positions of recognisable local group galaxies.

Further possibilities are offered by globular clusters and pulsars. 

The colour-magnitude diagrams and chemical compositions of globular clusters are all subtley different, which should enable their identification. They are also spread in a roughly spherical distribution around the Galaxy. 

Radio pulsars have unique pulse shapes and timing properties that make them readily identifiable. A possible/probable problem is that many pulsars would be rendered invisible by the change in viewing angle.

In both these cases, a map of the revised spatial locations with respect to the ICRS should enable you to work out where you are compared with the position of the Earth now. I am unsure what precision could be achieved, but then we are unsure of our present location with respect to distance to the Galactic centre by a few percent.