The most popular place in Menorca to see a cruise ship come toddling in to shore is the small city of Mao (in Catalan; Mahon in Spanish). In response to the bumbling tourist parade that crowds the harbor, most businesses are of the tourist variety and therefore will provide little insight into the island's culture. The good news is that this has allowed for a decent collection of dining and nightlife establishments to thrive along the harbor-side Moll de Llevant, making it not only an attractive area stacked with the classic Spanish facades of buildings, but also a great place to hang out for the day and make fun of the cruise ship types.
You can do this from the terrace at Cafè Sa Plaça, over tapas and wine at Can Vermut, or at a place that tries too hard to rip off the Hard Rock Cafe, but may still be worth it for the craft beer (Rock and Beer). Our suggestion is to make this a stop somewhere in the culture mix (visiting the ruins of Trepucó, the many city plazas or the array of beaches); therefore you won't feel too dirty brushing elbows with the folks jumping on and off cruises.