It'd very likely depend on location, aetheryte access, and the interests of the date. With his inexperience, he'd be more likely to go with whatever they suggested if they had an idea. If he had to pick...

In Eorzea, it'd probably be dinner at the Bismarck, a night at the Gold Saucer, or maybe a show at the Amphitheater.

In Ishgard, it'd probably be just some sightseeing. The city is full of vistas for long walks.

In Thavnair, they'd probably either go shopping in Radz-at-Han's bazaar or go sightseeing out in the wild proper. He was taken by Thavnair's natural beauty when he first arrived after all.