Purely for walkabout purposes I would choose the following (in that order):
1) Nikon 18-200 VR/3.5-5.6
Simply, great quality lens for the price had
second hand. Everything you would want bar a fast aperture. This would be my top of the list go to lens for walkabouts hands down. Slightly out of budget but worth considering.
2) Tamron 17-50/2.8
This one is everything you would want bar telephoto range.
3) 35/1.8
Nice FOV for a dx body therefore useful for lots of purposes. Really nice bokeh. Drawback for me is that it's a prime and therefore not always the best option.
4) Nikon 18-70/3.5-4.5
Useful range, sharp, manual override and generally superb optics. Drawback - slow aperture and no vr.