The 24-70 is heavy and attracts attention; the 24-120 gives up a stop but has VR; the 28-300 surrenders light gathering capability and a little wide angle capability, and there are of necessity, trade-offs in a 10:1 zoom ratio lens. But all things considered, the last lens offers the greatest versatility. You may want to consider a WA zoom or prime for the short end if you anticipate a lot of crowded scenes, or even a 35 or 50mm prime for low light. Consider your safety and the potential risk that goes with attracting attention as well. You didn't say where you were headed, I believe. As a Navy vet, I have traveled the world, and there are places I simply would not take anything other than a P&S.
After all day, the camera gets to be big and heavy too and a bit hard to disguise....
I use my 24-120mm f/4 AFS VRII frequently. It's a great range and the VR is a significant advantage in a fast moving travel situation. I've recently started using a Black Rapid strap and that's made a huge difference in my ability to carry the load all day. The strap is secure and easy to use, but the carry is exposed. Prior to that I've used a Domke J803 bag that's literally been all over the world with me. I work from the bag and "holster" the camera after each use. It's nice to have both options at your disposal.
Regardless of zoom choice, I also take a fast prime lens to give me the option of "skinnying" down the camera, especially for after dinner walks. The focal length is a matter of choice, but my personal preference is the 35mm f/2 AFD lens. It's a bit dated, but light weight and certainly sharp enough in the center to create good images. It's a standard reportage lens, but now replaced by the 35mm f/1.4 AFS lens which is huge (size and weight). My other choice is a 50mm f/1.4 AFD. These two AFD lenses work well on the D700, are compact and both still adequate in the optics department.
Roger It's still, ISO, aperture and shutter-speed, right?
I have been to Central and South America many times and I always took my best equipment. What is the use of having good lenses, if you only use them to take shots of brick walls in the privacy of your backyard?
To ease your concerns I suggest you insure your gear. This is fairly cheap with a rider on your home owner's insurance - I pay about $65 pa for K$20 of equipment.
It makes a lot of sense when you said "good lenses only to take shots of brick walls of your backyard....." The lens are for use it and take it with you around wherever you go..so I made the decision of taking the 24-70 and the 70-200 and take the chances....
Great idea to also take the 70-200, this allows you to put some distance between you and the object. I attach an example from the crowded market in Otavalo, Ecuador, where I only used the 70-200 with my D700.
I have a 700 with a 28-300 . It is a heavy combination, but I solved this this problem. Buy a Sun Sniper Sling. It is easy to carry your camera and it has a metal cable that makes it impossible for thieves to cut the sling.
I am writing this response from Uganda, where I have brought my 24-70 for use on my D700. I have used this lens here for the past two years and in other places such as Sudan, Botswana, etc. I agree with others who say that you should use your best equipment possible, or why have it. Of course it is large and heavy, but the results are worth the effort.
I have never felt threatened in terms of safety and have never found any need to hide or disguise my equipment.