Lens for landscape and zoom?

I'm looking for a lens for landscapes (wide angle) and zoom. I use a Nikon D3100 but will be changing to a D5200. I'm not sure which lens will be good for landscape photos as I will be traveling soon and plan to take many landscape photos. I already have macro/micro and portrait lenses so I do not need those. I'm looking for a lens or lenses under $700 in case I may end up buying two lenses. So far I have looked at:

Tokina 11-16mm f/2.8
Sigma 10-20mm f/4-5.6

Of course, I would like a more expensive lens, like the Nikkor 12-24mm, but I'm on a budget for the lens.

Tokina far and away out performs any other third party lenses.

http://www.kenrockwell.com/...6mm-ii.htm

I have the Tokina and it is one of the best lenses you can buy for a DX camera. You will not notice any difference between 10 and 11mm, less than 4%.

Here is a review on the Tokina showing the difference between 10mm and 11mm.

http://www.althephoto.com/lenses/superwide.php

Also, know that there are two versions of this lens, a DX version and a DX II (DX2) version. The DX II is the newer (and more expensive) of the two, but it has an internal focus motor, which is required for your camera to autofocus the lens.

I have the original version, but I also have a D90 - with a focus motor in the camera, so the original will focus on my camera. But your camera does not have the internal focus motor, so you need the DX II lens which has the focus motor in the lens… Basically equivalent to AF-S lens.

The Tokina is awesome, i use it myself. It even works on full frame/film cameras at 15-16mm. Be aware that there's a version of it with in-lens autofocus motor, but autofocus is uncritical for ultra wide lenses anyway. Here is a sample shot. Handheld, 1/30s, ISO320, f/4:

Note that it's sharp even in the corners - a rare thing among ultra wide angle lenses.

The Sigma 10-20mm f/4-5.6 is a fine choice too - surprisingly it has better reviews than the more expensive f/3.5 version.

However, also consider the new Sigma 8-16mm. It is not a fisheye lens, and 8mm is another step up in wide angle capability compared to 10mm.
Here is a review:
http://slrgear.com/...330/cat/31

Of course, it will strain your budget to the max… But ultra wide angle lenses are always expensive.