Realize that every aspect of photography involves trade-offs. Choosing the ultimate lens involves considering the subject matter, venue and working habits, mobility and price. The best lens is the one that involves the fewest trade-offs.
The 18-200mm would be a difficult lens to beat for travel. Tremendous versatility in a single lens. It also means less lens-swapping, for convenience and keeping dust from the sensor. VR is worth its weight in gold and sharp images at low shutter speeds for available darkness shooting. It only weighs 560g making mobility excellent. I greatly enjoy working with this lens. As a "street" lens, the image quality is far more than just adequate. I expected much less when I bought it.
The 70-200mm VR is without doubt a very fine lens, and worth considering if you regularly make very large prints, shot off a tripod. The constant f2.8 would also be nice for very low light shooting, hand-held with VR. The downside is that it is priced as the professional lens it is, and adds 1470g to your camera bag. If there is a D3 or D4 in your future and budget is no problem, it certainly is a no-compromise lens.
The 80-200 is slightly lighter at 1300g and a whole lot less money. However, it does lack VR which means a need for high shutter speeds. If you are very steady, you may be able to get away with 1/125th at the 80mm end, but would need at least 1/300th at the 200mm end for hand-holding. Though the design goes back to 1996, it still is a fine lens and it too would work at full-frame with a D3.
As a general purpose lens and specially for traveling, the 18-200mm is hard to beat. Between half and a third the weight of the others and capable of amazing quality for an 11x zoom lens. While it is slow at f-3.5-f-5.6, VR makes up for it. I have sharp pictures shot in very difficult venues at the 18mm end at f-3.5 at 1/4 of a second. A lot less easy, but have done 1/4 second exposures at the telephoto end as well. If possible I shoot a burst and go for the sharpest at that end of the zoom. What it may lack in ultimate image quality compared to the 70-200mm it more than makes up for in convenience and versatility in hand-held photography.
For ultimate in image quality, I have a number of prime lenses - which I rarely use. They only show their superior quality when used off a tripod and printed large. For web and e-mail use or for prints to be viewed at reading distance, the inconvenience overrides the value of the extra sharpness. Unless one can shoot at very high shutter speeds, the sharpness of the glass is nullified by even small amounts of camera movement when hand-holding. The 70-200 with VR certainly helps a bunch - but at a great cost.
I added the pro-level 12-24mm to the 18-200mm and have the perfect walkin' 'round kit. It adds just 465g and gives me the 35mm equivalent of 18-300mm in two relatively compact and lightweight lenses. I can not imagine a better travel kit, unless I were exclusively shooting landscapes, and traveling to the spot of each shoot by vehicle. I would have no hesitation to submit an image from this kit to any editor. At the end of a day spent mostly on foot, weight - and thus mobility - really matter. It would also be a superb set up for a sports/action shooter.
Were I traveling under circumstances that would let me do uncompromising contemplative photography under ideal lighting conditions, using a sturdy tripod as much as needed, the 70-200mm would have the edge over the other two. The 80-200mm is also a very good lens, but lacks VR so supports are needed unless light is perfect for the lens. However, if working in this ultimate quality/no compromise way, the 18-70mm would need to be replaced with the 17-55mm f-2.8G to match the quality of the 70-200. It weighs 755g compared to the 18-70mm at 390, so you pay the price in weight as well as money.
With the 70-200mm and the 18-70mm along with the D200 body, you are carrying 2780g, compared to 1480g with the D200 and the 18-200mm. The 80-200mm would only lighten the burden by 170g. My combination of wide-angle and super-zoom give me a weight of 1945g with the D200, which I consider a reasonable price to pay for the ultimate in versatility.