My advice with Nukes is to not piss around.
By launching just one nuke, you've already initiated retaliation from him, and possibly from others. So you might just as well launch all the f**ckers and be done with it.
If you plan to start the nuking, then save up some money, and search all of his cities. Find out where his forces are concentrated, where his money is coming from, and most importantly, where his nukes are. Compare notes with your military advisor until you've accounted for all the ICBMs. Make sure all those cities go on your targeting lists. Check if he has any tac nukes unaccounted for. If so, watch out for his subs - spend money on troop plans and find out where they are. Destroy them too.
If you can then avoid other civs declaring war on you (use methods given above), you will have a completely prostrate Civ on his knees, with no/very few nukes left. If you've got SDI, that's very little damage in return.
All you've got to do then is just hope that climate change is kind to you, and that your forests get changed, not your grassland, as your population growth will have already peaked with many cities having little or no surplus by the modern era.