I was looking for the same thing earlier this year to use with my D300, for mostly landscapes. The equivalent DX format lens to a 24mm would be a 16mm. My research brought me down to 3 lenses: The Nikkor 14-24mm f2.8, which is a pro lens and costs $2000.00 (too expensive for me). The Nikkor 16-85mm f3.5-5.6 ED VR that costs $700 list. And the Tamron 17-50mm f2.8 (the non VC, vibration control, version got better marks for sharpness) wide range of prices on line, but the low cost leader of the three. What I ended up choosing was the Nikkor 16-85 because of its very good reviews and low distortion at 16mm. It's not fast but I don't really need a fast lens for landscapes as they don't move very quickly. The Tamron got good reviews also but I decided to stay with Nikon for a number of reasons that I can go into if you like. That's my 2 cents worth.

All zoom lenses have compromises in lens crispness when compared to prime lenses of same length. Usually, the longer the zoom range, the less crisp, especially away from center at wide open aperture.

I suggest that you test.
Set camera on tripod. Set lens to wide zoom. Take Aperture Priority photos at a few different apertures (the camera should balance exposures to near same).

Repeat at mid-zoom and narrow zoom.

Now critically compare corners for sharpness. Then compare centers for sharpness.

You may find your "sweet spot" aperture, and your best zoom length length.