First Nikon d5100 lens upgrade?

I have the kit 18-55mm lens, but I'm not satisfied with its low light performance or its limited zoom abilities.

For low light as well as great overall performance, I'm considering the 35 mm prime lens. I've heard great things about it. Thoughts?

For a sharper and more versatile lens with zoom capabilities, I'm thinking about trading in my 18-55mm (I know it isn't worth much) and opting for either the 16-85mm, the 18-105mm, the 18-135mm or the 18-200 mm. Which of these, in your experience, would be the most useful and versatile? Which of these is the sharpest?

Overall, I'm looking for two great travel lenses that can accomplish a lot without having to lug a mountain of gear around with me.

Added (1). Edwin,

thanks for the response. Assuming that the 35mm helps me out with low light for now, which of those other lenses would be best for a nice zoom range, low lighting not being a factor?

If you're unhappy with the performance of your 18-55mm zoom in low light you'll be just as unhappy with any of the equally slow variable aperture zooms you listed.

If you want a fast zoom you're going to have to dig deep into your pockets. The Nikkor AF-S DX 17-55mm f2.8G ED-IF is about $1, 400.00. The Nikkor 70-200mm f2.8G ED VR II is about $2, 400.00.
Note that the 17-55mm doesn't even have VR.

For low light photography buy the 35mm f1.8G. Keep your 18-55mm for general use.

Get the 35/1.8 Nikkor. Or a faster zoom, f/2.8 throughout the zoom range. As far as swapping out your 18-55 for an 18-70, 18-105, 18-135, 18-200 etc. I think you'd be surprised, all those Nikon Nikkor 18-to-somethings are designed to be "kit" lenses on various Nikon bodies and performance will be about the same as the lens you are now using. Exception being the VR versions which will permit hand holding while shooting at much slower shutter speeds.

(And hang on to your 18-55, you'll someday want to trade-in or sell your D5100, it will sell better with a kit lens attached.)

I've heard mixed reviews about the 18-55mm. I used to think they were cheap lenses that nikon threw in with the d40/x, d60, d3000, and so on. A teacher of mine said it was his favorite lens because it's "sharp". I didn't see it myself, but other seemed to agree with him.

I too thought about the 35mm. You should try it out and see what the frame looks like through the viewfinder. I was almost about to buy a 35mm until I tried it out in person. I didn't like the wide perspective, and the distortion of the lens was just not my thing. So I got the 50mm 1.8 and 1.4 (both quite good in low light situations).

I love nikon mostly for their choices in lenses. I've been starting up a collection of E series lenses. This was for photographers who don't have enough bang in their wallets; hence, E for Economy. I snagged the 100mm and 105mm e series, and I love them. Older lenses seem much sturdier to me compared to the newer, plastic-heavy lenses.

For zoom lenses, if you have the money, get 12-24mm dx or 18-200mm dx.

Hope that helps.