I would like to point out that you are all comparing a 1940's armored BB in capability to a 1980's or later designed missiles.
That is similar to comparing a 1900's dreadnought to 1860's monitor...
If you want to have a realistic evaluation of what a newly designed BB could do you would actually need to design a BB, including but not limited to using "more expensive than gold" armor as well as top of the line missile and torpedo defence systems. Either way designing and building a new BB without it being a CLASS of ships not just one ship is unlikely and designing a new class of BB's to be built is even more unlikely.
But yeah, assuming you started to design a BB right now and had unlimited funds to sink into it, lets say pres B decides that we need something that is big, black and shiny! you would end up with one hell of a ship that would not go down with one cruise missile, with the latest ballistic missile defence systems, especially the types shown here
http://www.youtube.com/watch?v=9V1pkTMCZ0M with a little bit of more power and dev could make it "one heck of a ship".
But then again, at the price of developing and building just such a vessel you could build hundreds of F22's or F35's so its unlikely to ever happen due to the financial constraints but there is a specific niche that it could fill. That niche is "cheap to use coastal bombartment and with modern weapons up to 50+ miles inland" the expense for supporting field units would be about 1-2% of what they are now and marines could literally order a shell for every opponent and with present cruise missile prices, they cant.