Hmmm. Interesting question. You want something that's versatile, comfortable, and that doesn't look too dorky when out for dinner someplace. Does that sound about right?
Maybe something such as the Keen Alki Lace ($95). I'd call these an "urban trekking" shoe, with all-leather construction, grippy outsoles, durable enough to take some hiking and cave tours. Low-cut, so they'll get wet in the jungle perhaps, but that's going to be an issue with most shoes out there. Merrell's Sight ($100) shoes take the outdoor angle a little more seriously, with a sole that's obvious pried off a hiking boot, and a little "tougher" look. But they'll still serve you well when trekking through the airport.
On the women's side, check the Keen Toyah ($90) and the Merrell Quartz ($95). Very similar shoes.
For something that's a bit more backcountry-oriented, try the Oboz Sawtooth ($135). These are a midweight hiker, very comfortable, with grippy outsoles and more support than you'll find in a low-cut shoe. The Merrell Col Mid Waterproofs ($145) are the same height, but look a little more like a street shoe than the Oboz.
For your companion, analogous shoes would include the Lowa Bora ($175) and Oboz Yellowstone ($125)—again, midweight hikers that are bit more trail-friendly than low-cut shoes, but still light and comfortable and not entirely out of place in the city.
Hope that helps! Have a great trip.