Two reasons why I vote no:
1) Several ports in the world are established "nuclear-free" zones and forbid the operation of such vessels.
I think it is more important for the Navy to maintain geographical flexibility - the ability to deploy their most powerful surface warships to any coast in the world.
Imagine if New Zealand was struck by a natural disaster and the USN deployed ships to provide aid (think Indian Ocean Tsunami 2004). Any nuclear-powered vessels would have to detatch and idle in the distance.
2) Almost spot on what baggygreen said; terrorists have already punched a nice big hole in a conventionally-powered DDG. It is naive to think that this can never happen again. It would be quite a coup for a nuclear-powered vessel to be stricken while making call in an angry foreign port.