Simple, elegant, and classy is the way to go. Flashy and big is not. And, while I absolutely acknowledge that many watches are far more interesting and desirable to an afficionado, I like millwright79's latter two suggestions the most for gifting to someone who isn't. And, I'd probably even consider the Datejust before the Explorer 1. Go with the brushed oyster band and smooth bezel. I'd also opt for the roman numeral markers. This combo is elegant, classy, yet understated. Now, personally, I happen to really like this combo with the dark blue dial, and think it'd be excellent in black as well. The Aquaterra suggestion is also excellent, IMO, for all these same reasons. But a non-watch-enthusiast is far more likely to be wowed and impressed with a Rolex than with an Omega IMO.
Here's an example (and albeit not a fabulous pic) of the Datejust combo I like. I am not necessarily recommending a used watch (although I don't think it's a bad idea), but this is a used piece from 2002 on Timezone priced at $2200 right now to illustrate what I consider a sharp gift:
Although I do prefer the contrast of a darker dial against the brushed stainless case and band, it does also looks quite nice with the Rhodium dial IMO (this one is priced at $2900) -