I think this may be "The Cabinet of Oliver Naylor" by Barrington J. Bayley...at least it's reminiscent.
The computer simulation is called the "thespitron" and to modern readers it resembles nothing so much as Star Trek's holodecks. The story even starts out with the protagonist in a film noir detective story like the ones Picard enjoyed.
The spaceships are called 'habitats' and the FTL drive is called the 'velocitator'.
The protagonist and his friend do locate and dock with another habitat, and they do have dinner together. (The society is kind of a neo-or-revived-Victorian one). The person from the other habitat does, indeed, slowly reveal himself to be crazy.
The crazy guy uses his 'zom ray' device to push the protagonist's habitat up to such a velocity that his 'velocitator' can't cancel it and the habitat shoots out to the edges of the universe far from any galaxies.
At the end there is some problem with the thespitron. It ends like this.
Derived of the massy presence of numerous galaxies, the signposts of reality, the thespitron had ceased to function.
The closing circles were getting smaller. Now there was only the shell of the habitat, analogue of a skill, and within it his own skull, that lonely fortress of identity. Naylor sat staring at a blank screen, wondering how long it would take for the light of self-knowledge to go out.
The story's quite dense and complicated and I probably haven't explained it well. But if this is it, I am betting you will recognize it at once, it's not like any other story I know.