Huck, most of the lenses out there can get you great results. It really depends on the focal length you need and the maximum aperture. Faster aperture lenses usually raise the price but aren't always as sharp as the cheaper lenses. Zoom lenses also tend to be more expensive than primes. If you want sharper images, each lens usually has a sweet spot in terms of the right aperture to use. The first thing you should consider is the focal length. If you want a wide angle or fish eye, Nikon offers the 10.5mm or the 10-24mm...both of which are kind of pricey. Unfortunately, so are other zooms close to them like the 16-85mm and the 18-200mm. Both zooms are leaps better than the kit lens though, so it's worth considering. The only lenses that are relatively inexpensive and works with your camera I can think of is the 35mm f/1.8 & 50mm f/1.8. You can always go with Sigma lenses which run a bit cheaper.
I'd also look at
500px is Photography and check out what others have done with the equipment they have. Type in "landscape+D5100" in the search. It usually shows the meta data for each pic.