Best budget nikon lenses for landscape photography?

I got a Nikon d3100 for Christmas and it came with the standard 18-55mm kit lens. This is a good multi-purpose lens, but I'm more of a landscape photographer. What is a good telephoto lens for this style of photography? I'm on a tight budget here so I can't break the bank!

Landscape needs a wide angle lens, one that sees at an angle more than human eyes can see. That's the beauty of the kit lens. At 18mm, landscapes can be easily taken without too much distortion. No need to go to the bank. All you need is already in your hands.

http://keerok-photography.blogspot.com/2011/05/lenses-so-many-of-them-there-is-no-best.html

Stick with the one you have got. Just buy a few filters for it, maybe a neutral density filter would be a good buy.
A neutral density filter will help you to use slow shutter speeds, thus making waterfalls for instance, look awesome.

If its more landscapes you want, instead of going telephoto why not go even wider. Try a Nikon 10.5mm fisheye. You can't help to get good landscapes with this.

You don't want a telephoto lens. If your 18mm is not sufficient, then you need a super-wide angle lens.

In my view, the best super wide angle for a DX camera is the Tokina 11-16mm f/2.8. But you can't autofocus it with your camera as your camera does not have the required in-body focus motor. And at $700, it is not necessarily cheap.

The least expensive but good lens for your camera is perhaps the Tokina 12-24mm f/4 DX 2. Make sure it is the DX 2, which is a bit more expensive than the DX, as the DX 2 has a built-in focus motor similar to a Nikon AF-S lens, which means you can autofocus with it. The less expensive Tokina 12-24mm f/4 DX will not autofocus with your camera.

The lens is about $600, and while not cheap, it is the least expensive good lens. In contrast, the Nikon AF-S 10-24mm f/3.5~4.5 is $900, which is a lot more expensive.

An alternative might be the Sigma 10-20mm f/4~45.6 EX DC HSM at under $500, but I'm always a bit wary about Sigma.

And make sure these lenses are for the Nikon mount as they are made for several different manufacturer's cameras. At any rate, your are going to spend $500 to $900 for a good lens.

Avoid putting cheap junk lenses or lens/filters on your camera, as you will only end up with a cheap looking photo. If these lenses are out of your budget, then save up for them while learning how to use your camera more. You might find that your 18mm lens will be sufficient.