I think this may be "[The Cabinet of Oliver Naylor][1]" 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 'velocitator' is capable of stupendous speeds, at the beginning the protagonist is traveling at c<sup>186</sup>...


> While waiting, he glanced through the window at the speeding galaxies,
> then crossed to the velocitator control board and peered at the
> speedometer, tapping at the glass-covered dial.
> 
> "Will we get there soon, do you think? Is 186 your top speed?"
> 
> "We could do nearly 300, if pushed," Naylor said.
>
>......Velocitator speeds were expressed as powers of the velocity of light. Thus 186, Naylor's present speed, indicated the speed of light multiplied by itself 186 times.

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.

The protagonist gives up and decides to lose himself in the thespitron world.

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 skull, 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.




  [1]: http://www.isfdb.org/cgi-bin/title.cgi?41962