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Very tough choice, if you were truly limited to one lens then you'd have to prioritize what shooting is most important to you.
**Inside buildings - 16-35 / 14-24 / I only have a 17-35 and that worked fine with higher ISO's.
**General all-in-one, if you can only have one lens - 24-120 f4 VR.
**Tuscany - a long lens is really beneficial here, though if you buy a high res D800 (you did say budget did not matter) then you could stretch the 24-120 with cropping.
I left my 70-300 in the hotel other than in Tuscany and Cinque Terre.
The 17-35 saw action as described above (mostly indoors, some outdoors)
The 24-120 was the most versatile, most used, but I tend to find 24mm plenty wide other than indoors.
Other option - bring one DSLR lens that covers your top subject priorities, and a P&S to cover the rest. Primes are great, I enjoy them but I don't like visiting places I don't have easy repeatable access to (like Italy) with just one prime.