There can be only one.
With the constraints of a single zoom VR lens for travel with a Nikon DX camera, the only choice is the 18-200mm.
Loren makes a critical point that this lens will not go ultra wide. I have found this to be a bother on some occasions. However, the 1.5X sin is inherent in the DX format. They are simply the wrong choice of cameras for wide-angle photography. Nor are these cameras the right choice for printing posters. The 18-200 has all the sharpness needed for excellent 8x10 prints or 1800 pixel wide web images.
There are other troubles. The lens is slow (f3.5), heavy, and bulky. It doesn't close focus for micro photography either. I had to buy a special long snoot, soft case to protect it on my D200.
However, for travel it gets the job done like no other. Over a 10 trip to D.C., I made thousands of exposures of tight museums, dim train stations, huge monuments, active performances, and wide vistas. The 18-200 never came off. We were walking 5 to 10 miles a day and left the camera bag at the hotel. So I spent zero time luging/juggling camera accessories, and far more time enjoying my trip.
I also use this lens for my New England waterfall excursions, gardening, and culinary images. Can't beat it for skiing and boating. It went with me for a week of bread baking school at King Arthur. It was just fast and long enough to capture speakers at an astronomical conference at CalTech.
Recently I caught a conjunction of the Moon and Jupiter by bracing against the bulkhead of a ferry crossing Lake Champlain. Howbout that for VR!
One last word about the utility of vibration reduction. Unlike Dorien, I find it useful at all focal lengths. Especially hiking around at this dreary time of year, VR lets me get sharp images at 1/8 sec shooting freehand. Even zoomed out to 18mm, it means not losing a nice image to motion blur at sunset.
Regards, Fred