If you liked the 16-85 on your D300 then you will like the equivalent 24-120 f4 on your D600 even more. It is likely to be sharper and the constant aperture is nicer to work with and of course, you will have twice as many pixels in each image when compared with the 16-85 on D300. The build quality of the 24-120 is good.
If you are hiking/trekking to your landscape locations then weight and portability start to count. The 24-120 has VR and it is both lighter and shorter than the top-of-the-range 24-70 f2.8. For lanscapes you'll seldom need the speed of a f2.8 - you will likely be shooting stopped down most of the time.
On the wide end, I recently looked at the 14-24 f2.8, the 16-35 F4 and the Tokina 16-28 f2.8. Of the three, only the 16-35 f4 takes a screw-in filter - the others require fairly expensive adapters for fitting square filters and you need the large sized filters too. They are expensive and more likely to be damaged in transit to shooting locations if you are hiking there.
The 16-35 is by far the lightest of these 3 but if weight is an issue you can also consider the inexpensive 18-36 AF-D which is very light and relatively inexpensive (I have one).