only one Nuke?

You only get to build one ICBM? (the free one that comes with the Wonder)

if so, then what's the point of the SDI building that's available for every city?

To prevent that one nuke from completely destroying the city. You can avoid building them if you can get the nuke yourself.

Since that one nuke can potentially destroy any city (except a capital which is reduced to a population of 1 and has all its buildings, wonders and great people destroyed), you need the SDI to protect each city as you don't know which city the nuke is going to be targetting. Also, if you have the Taj Mahal wonder or the Eiffel Tower wonder, the SDI contributes to an increase in culture and science respectively.