Awesome idea. I've got my beer and peanuts standing by for the trip. As for the random destination. the Msss MFD v2.0 might help for out of system travel. As for the random location in the system not sure how but you could possibly use the number typed into the MFD to actually be a random number string so that the end results are the same each time you use that particular number.
As for the process it should be a random and absurd as possible. If you typed in 100 trillion to one for example the computer could speak back and announce events like; ” Probability 10 trillion to one” and “there are a bunch of angry penguins in the cargo bay” “Probability 1 trillion to one” and you see a whale float in front of the view screen “probability 100 billion to one” and if you happen to look at the outside of your ship the mesh is a tea cup……until you do arrive at your destination.
Or you input some number giberish, or have it choose some itself and it chooses an X Y Z, dX dY dZ and UTC time to place your ship at. CTD and worse weirdness should be par for the course.