My recommendation on a 'walk-around' lens would be something with a wider zoom range. Tamron, Sigma, Nikon, and Quantaray all make an 18-200(+) lens that covers the complete zoom range of the standard kit zooms (18-55mm + 55-200mm).

Of those makers, the Nikon product is the best, however it is also the most expensive. I've got a Nikkor 18-200mm VRII slowly moving across the country to me via UPS ground, and I'll post some thoughts/pics from it once I get it and get out with it a bit.

That 28-70/f2.8 is nicely fast, but the zoom range suggests to me that it is intended for full frame cameras (28-70 is basically the same FOV as the 18-55mm lens on APS-C sensor), thus 28mm on the D60 would not, at least for me, be able to get near wide enough for something that I would be using as an 'all-in-one' lens, let alone the limited zoom. For me, an all-in-one lens covers both the wides and the tights.

I haven't been able to use it myself, but from what I've read, the Nikkor 16-85mm is supposed to be the best quality (read: technical performance) 'kit' zoom for DX cameras, though it weighs in at a hefty $600.

In short, my opinion is to go with a 'super-zoom' lens, i.e. 18-200+mm. Depending on the brand you buy, you'll spend anywhere from $400 to $800, and the quality in fit, finish, and imagery, is sure to reflect what you pay when in the world of 'super-zoom' all-in-one lenses.

On the other end of the spectrum, as HSLD suggested, you could easily just spend $200 and get the wonderful 35mm f/1.8 and practice using your feet to 'zoom', and thus become better at composition and judging scenes. I love my 35, but I also love to be able to zoom in tight with a long lens when I don't have the ability to hoof it.

My travel kit, once my new lens arrives, will be the 35mm and the 18-200mm. Everything I need.

Food for thought.