I'd either look at the 17-55mm f/2.8 zoom, a 35mm f/1.8 or 50mm f/1.8 prime.
Nikon did a really nice 35mm f/1.8 DX lens which was sharp wide open and delivered excellent IQ. The 50mm is also an option as it's fairly cheap for a prime and versatile - easily the best value for money lens I've ever bought, but might be too close to 70mm which you already have covered. I'd personally stay clear of the Nikon 24-70mm f/2.8 (especially if it's the older G type non VR lens) as it's very bulky, heavy, suffers from considerable CA with purple fringing off centre and is only sharp in the centre area of the frame. To avoid the CA you really need to step down the aperture and this lens is bang average at the short and long focal lengths and optimal at 50mm
I personally found a small light fixed prime like 35mm or 50mm much better in all aspects. If you're using a crop body I'd go for the 35mm or 50mm prime, they're cheaper, sharper, lighter and just overall better. There's currently 2
second hand Nikon 35mm f/1.8g AF-S lenses on Wex website right now for £76 & £80, 2
second hand 50mm f/1.8g primes for £81 & £85, whereas with the 24-70mm f/2.8g I'm seeing prices between £350-£500. Maybe get both the 35mm and 50mm and you'll still save at least £200 over the 24-70mm.