18-135 vs 18-105
Never tried a 18-105 but I have the other two. The first 18-135 I saw was on a demo D80 in a Circuit City (remember them) and it was AWFUL! I pointed it at the array of rectangular windows at the front of the store, and the barrel distortion at 18 mm was amazing - I was astonished that Nikon would produce a lens that bad. Then I zoomed to 135 and was just as amazed at the pincushion. I was considering the D80 at the time and decided not to buy because of the lens.
Then Santa (or more accurately, Mrs Santa) gave me a D80 that Christmas. When I saw the box, my reaction was "oh no! how do I explain to her that the lens is junk?" But when I looked thru the lens on the gift D80, there was no distortion visible in the viewfinder! And it turned out to be an all-round excellent lens. So - take this away from here - they aren't all created equal - try the lens on your camera before you buy.
I got the 16-85 despite my high opinion of the 18-135 mostly because of the VR - a personal problem with advancing arthritis and difficulty hand-holding any more. And I also liked the wider end - it really does make a difference in many situations, especially indoors. As good optically as anything I own, too. The short focal length on the long end isn't an issue as I also have the 80-400 VR.
You decide: is the wider 16 mm more valuable to you than the 18 mm?
You decide: is the 135 longer end more useful than 85 mm?
You decide: is VR important enough to spend the extra money? Your post sounds like VR isn't especially important, but it can open up lower light shooting opportunities you might bypass today.
You decide: is the cost of the 16-85 an obstacle?
Decisions: the budget approach is the 18-135 - just make sure you try before you buy, and you could get a really good lens for a budget-conscious price. The 2 lenses can be optically pretty close to equal if you find a good 18-135, and if so, it boils down the which lens has the more useful zoom range, and whether VR is of value to you.