A better lens than the 18-55 kit lens?

I bought a Nikon D5100 body. I don't wanna buy the 18-55mm kit lens. Can anyone suggest a much more capable lens that's sharp and not so expensive?

Well its really depends on your price range. But the 18-55mm is really not as bad as what people think. It offers good wide-angle to portrait. It does suffer in low lighting though.

AF-S DX Nikkor 18-200mm f/3.5-5.6G ED VR II ($829.95) Yes this is expensive but this lens is sharp, gives good quality images, and covers the wide angle 18mm up to the "zoom in close" 200mm. This is expensive but its kind of a 2 in 1 as most are 18-55mm and then have to get another 55-200mm or 70-300mm.

Nikkor AF-S DX 55-200mm f4-5.6G VR($288.97) Good for zooming in close for far subjects with the 200mm, and the 55mm allows portraits to be done. However this lens will suffer in low lighting like the 18-55mm.
Nikkor AF-S DX 55-300mm f/4.5-5.6 VR II($382.57) Similar to above, closer zoom, will suffer from low lighting.
Nikkor AF-S DX 18-105 mm f3.5-5.6 ED VR($337.88) Wide-angle shots 18mm to somewhat good zoom =P at the 105mm.

Nikkor 10-24mm f/3.5-4.5G ED($899.95) Cheapest wide angle lens i could find that's under $1000 made for DX camera format (your D5100 will be good with any DX lens).

Nikkor AF-S 50mm f/1.8G($232.88) and Nikkor AF-S DX 35mm f/1.8G($259.35) are prime lens', meaning they are set at one focal length and do not zoom in and out, in order to zoom in/out you will have to physically move the camera closer/further from the target. Now these lens give superb quality pictures, very sharp, very fast, performs well in low lighting, and gives great portraits. These lens i would only suggest if you already have a zoom lens. I don't suggest these as first lens to use (unless you're going to buy another lens) cause it can limit you because its set at 50mm or 35mm. With other zoom lens you get the choice of doing 18mm wide angle shots to zooming in to closer targets. This is set at 35mm or 50mm meaning its meant for portraits, but to a certain extent you can use this for other purposes as well. Once again these lens are really fast, and a favorite among many photographers including myself. (I use the 35mm since on DX we do not have full frames the 35mm is closer to 50mm, i use the D5000)

So yea comes down to what type of photographs you plan on taking as each lens will serve a different purpose, i haven't listed any macro lenses because i do not do much macro photography, but there are some that are within $200-$400. Also prices i have are not exact, their according to a store i go to, but they shouldn't be too far off from other places.

If you know exactly what you need go for it. If you don't understand what 18-55mm is then you probably would want to read this first. Sharpness and image quality is the responsibility of the photographer. The camera and lens are just tools.

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

Gee, the 18-55 is cheap in price and performs well. It close focuses to 11 inches as measured from the sensor plane to the subject which means it works well for flowers and larger bugs. It is a really good general purpose lens which is small - great when you want to travel light. You'll have a hard time beating the 18-55 lens in quality versus price.

18-55 costs $100, $140 with VR
Step up would be the Nikkor 16-85 at $600 (really nice general purpose range!)
Wide zoom range: Nikkor 18-200 at $800, but not as sharp as the above lenses.
All the above lenses are considered slow.
Sigma or Tamron will cover the above ranges for less money and worse quality.

or get much better performance with prime lenses…
35mm, f/1.8 at $200
50mm, f/1.8, AF-S at $220 (don't get the AF version)
One of Nikons f/2.8 micro (macro) lenses in the $500 to $900 range

If you want to have fun shooting animals, Sigma 50-500 or 150-500mm in the $1000 to $1500 range. The 50-500 is nicknamed the Bigma since it's heavy and big.

The above answers some it up quite well

As a superior replacement to the 18-55mm kit lens, consider the Tamron 17-50mm/2.8.It's not terribly expensive, and (except for the autofocus) superior in every way. It's a very popular lens.

It comes in a stabilized (VC) and unstabilized version. The unstabilized one is said to be sharper, but that's highly dependent on the actual copy of the lens, there seem to be big sample variations. I got the stabilized one and it's just as sharp as sample shots of the unstabilized that i compared them to.
If you go for this lens (either version), then definitely have it thoroughly checked out by someone who is experienced in photography, to ensure that you didn't get a bad apple without knowing it as a beginner.