The 16-80mm isn't a bad lens, but a bit overpriced. For your first zoom I'd recommend a kit with a cheaper lens like the Nikon 18-105mm or 18-140mm and upgrade from there.
I think someone else on this forum has experience with the Sigma 17-70mm which is a good value.
Another path could be full frame.
You can get a Nikon D750 kit for 2300. Full frame is a step up in image quality with a bigger sensor that captures more of the image.
If you put a full frame lens on then the "APS-C" rectangle is the picture you'd get from a D7200 and the "Full Frame" rectangle is the picture you'd get from the D750. Lenses like the 16-80mm however don't cover full frame so you would get black corners, but most Nikon lenses are "FX" and cover full frame. DX lenses only cover APS-C.
Full frame will have better low light because the pixels can be much bigger. APS-C is cheaper and advantageous if you need to get closer.
That Nikon D750 kit is 300$ more expensive than body only, but if you check ebay you'll see that same lens sold for almost 500$ so you should be able to sell it for a profit.