I try to keep the gear posts to a minimum, but, like everyone else, I'm always open to recommendations for new equipment. I think I'm pretty set with what I'm currently using, but in case you're in the market for some epic glass for your Nikon, I've compiled a list of what I believe to be the best options for a traveling photographer. A few of these lenses are (or have been) in my bag and are used often. Though I have not used all of the lenses listed below, I have researched enough to feel that I can recommend them all without reservation. It's up to you to decide what works best for you. Clicking the links and images will take you to trusted online dealers for the more technical information not listed here. As always, look around for the best price from a store you trust. Without further adieu, here are (in my humble opinion) Nikon's best FX (full-frame) travel lenses for under $1,000 USD.
Nikon 18-35mm f3.5-4.5 G (Under $800 USD)
The Nikkor 18-35G (the newer one, not the old "D" version) is my favorite wide angle zoom. The slightly wider and more expensive Nikkor 16-35 f4 is an excellent lens, but it's larger, heavier, and almost twice the price. I've owned this lens for years and have made some of my best images with it. It is light, well-made, takes 77mm filters, is very sharp, and at less than $800 USD (around $500 used), it's a great option.
Nikon 24-85mm f3.5-4.5 G VR (Under $500 USD)
The Nikkor 24-85G VR is usually available as a "kit lens" when you by an "entry level" (I despise these arbitrary marketing terms...) full-frame Nikon like the D610 or D750. It is very versatile for very little money if purchased separately. I've seen them used for less than $300 and have read some great reviews on it. I was considering this as a walk-around lens for city travel on my D750, but went for the Nikkor 24-120 f4 VR instead because it takes 77mm filters (the 24-85G uses 72mm). If the latter is just out of your budget, the 24-85G shouldn't disappoint as your go-to wide angle zoom.
Nikon 20mm f1.8 G (Under $800 USD)
The Nikkor 20mm f1.8G is a sexy lens. I've been drooling over it since it came out, but have been satisfied enough with my 18-35G that I haven't been able to justify buying it. This would not only be a great lens for wide landscapes, but the generous max-aperture of f1.8 makes this an awesome lens for nighttime and astrophotography. It focuses super-close as well, down to 0.66 feet.
If you're on a tighter budget, the Nikkor 20mm f2.8 AF-D is still a great option for under $400 used.
Nikon 35mm f1.8 G (Under $600 USD)
If I could only have (for some odd reason) one lens for city travel, I'd choose the Nikkor 35mm f1.8G. That 35mm focal length is probably the most versatile as far as fixed lenses go. It's not too wide and not too tight. I don't own this fast super-sharp lens, but I do have the Fuji 23mm f2, which on the cropped sensor Fuji cameras is equivalent to 35mm on a full frame sensor. I find that focal length really great for the majority of "street photography" situations. At f1.8, this lens provides really shallow depth of field while maintaining a reasonably wide angle of view.
Nikon 50mm f1.8 G (Under $250 USD)
My first Nikon lens was the Nikkor 50mm f1.8G. I picked mine up used for only $150 USD. I don't use it much since I don't shoot weddings or portraits anymore, but I keep it around for indoor, low-light situations when traveling abroad. It is a very small and extremely lightweight lens that packs loads of lustful sharpness for very little money.
Nikon 60mm f2.8 G (Under $600 USD)
Since we're keeping things under a grand, I couldn't list Nikon's 105mm macro lenses, but the Nikkor 60mm f2.8G is still a great choice. This has been called the "Swiss army knife of lenses" because it serves as a macro, normal prime, and great portrait lens all in one. On a DX (crop sensor) camera it has the equivalent focal length of 90mm, which should provide a good amount of working space between camera and subject without breaking the bank.
Fixed Telephotos & Zooms
Nikon 85mm f1.8 G (Under $500 USD)
If for some strange, out of my control reason I had to choose only three fixed-lenses from this list for my travel and landscape photography, I'd pick the 20mm f1.8G, the 50mm f1.8G, and this 85mm f1.8G. That would cover me pretty well with some arousingly-fast glass for a mere $1,400. (I wouldn't be shooting much wildlife with those choices, but this list is for globetrotters anyway...) The Nikkor 85mm f1.8G is an excellent portrait lens for an excellent price. The f1.4 version is much more expensive, but only provides a little more light...not sure about you, but that's not worth the price difference to me.
Nikon 70-300mm f4.5-5.6 E VR (Under $800 USD)
Before I bought my 70-200 f2.8 VR II, I owned the older version of the Nikkor 70-300 VR and really enjoyed it. I hear that this new "E" version is even sharper, focuses faster, and has more stops of vibration reduction. That 70-300mm range is great for versatility. If I had that proverbial gun to my head and could only choose the three zooms from this list, I'd be pretty set for every situation including wildlife (...still be having heart palpitations over that 20mm 1.8G though...). It'd be nice if the price of this lens decreased a bit, but it certainly packs a lot of features for less than $800.