Let's say that sometime in the future, technology has advanced enough to the point where we are able to create a controlled black hole and hold it open with exotic matter, creating an Einstein-Rosen bridge (please correct me if I'm using the wrong terminology). Assuming that we are able to keep the bridge stable and traverse through it - how could we actually figure it where to open the bridge to? Is there any way of doing that, theoretically, or would it just open at a random point in space-time? Could we control the coordinates at all?
Since this is entirely theoretical, the answer is whatever you need.
Usually the destination locus is either (approximately) controllable from the input black hole's parameters - mass, spin, electric charge - or it might depend on where the input locus actually is (for example, its position relative to the nearest star).
See the description of an Alderson tramline in Niven & Pournelle's The Gripping Hand:
Ships travel along Alderson tramlines. Tramlines form between stars, along lines of equipotential flux. I won't explain that, you got it in high school...
In other works (e.g. J. P. Hogan's Giants pentalogy), the hyperspatial projection of a gravitic vortex - an "open" black hole - is controlled through mass, spin and "other parameters". By manipulating the first two parameters, the exit point is positioned somewhere in a implied three-dimensional Newtonian isochronic continuum. By fluctuating the latter parameters, the terminus' fourth coordinate can be uncoupled from its default setting of "now" and land somewhen else.
In some cases (Hogan again, or the 'Second Takeshita Hypothesis' in David Weber's The Apocalypse Troll), a strong enough transition might land the terminus in a completely different universe.
Realistically speaking? Probably you'd make both ends in the same place, then move them around. It doesn't matter at all, though (the answer is "whichever is most interesting to you") - there are plenty of published worlds using both options, with nobody objecting. For some random examples, Peter F Hamilton's Commonwealth has wormholes that open to wherever you like (there's a scene in one book where some characters are rating new planets for colonisability by sitting in an office and opening wormholes into orbit above them for initial surveys, then onto the surface for more detailed investigations), whereas Iain M Banks' Algebraist world has wormholes made with the holes together then spread apart the slow way (and, indeed, the book is set in a system that has its wormhole blown up at the very start, and doesn't get it back until right at the end - because it takes a very long time to ship wormhole ends around slower than light - making this an exceedingly rare example of a space opera with (almost) no FTL).