If he doesn't get lost, yeah.

Laurence is good at navigating with a map. He will walk briskly over and peek inside the gymnasium.

There are: 

Squat racks and benches

Treadmills

Punching bags

A bouldering wall

(If Laurence was from the 21st century, and didn't notice the gravity control panels, he'd probably find this completely normal)

Are there people?

This guy is doing squats!

Presumably Laurence doesn't know this, but his form is not very good.

He's shirtless, wearing a pair of shorts.

The classical sense of "gymnasium," then.

Laurence will leave him alone and return to the cafeteria to meet Ensign Kim.

Harry is sitting at a table and waves to Laurence when he comes in. 

"Hey you made it!"

The mess hall is much more pleasant with waiting company. "Yes. I acquired a map."

"Wait, really?"

Harry looks it over. 

"That was a good idea, nice."

He's not sure why Ensign Kim is surprised by this -- isn't a map the obvious way to get around? -- but he lets it pass.

Time to converse. Inquiring further about Ensign Kim's life would be terribly rude without a clear opening, of course. He could ask more questions about the ship or Starfleet. It seems a bit early in the conversation to launch into an anecdote from his own Navy days, not to mention a bit early in the day and light on alcohol. He's still confused about how socializing works here. How about...

"When I was a captain I used to invite my young officers to dinners in my quarters. It was a regular custom among Navy officers of greater status, though of course some were more likely to extend invitations than others. Does Starfleet have any such custom?"

"Hmmm. Well to tell you the truth, I'm not sure I'm the best person for you to ask. I've been out of the academy for 2 weeks. I can tell you that the captain hasn't invited me to dinner, anyway."

"Should we grab some food? It looks like Tom's running a bit late."

"Certainly." How rude of Tom. Laurence will follow Kim to the replicator.

"Hamburger with fries, medium rare."

Laurence doesn't know what that is. So much for copying what Kim got.

He will again tentatively request "Roast beef," adding this time, "and potatoes."

Laurence is not exactly a simple man in the way of food -- he's been at many fine tables in his time -- but he is not exactly a creative gourmand, either.

The replicator apparently considers "and potatoes" to narrow things down enough, because it replicates some roast beef and potatoes without complaint.

Laurence accepts his magical fairy food and follows Kim back to their table.

"So how's it going? Computer helping you catch up on history?"

"I believe I have some better sense of things now. My schoolroom days are far behind me, but it seems I am to return to them more or less."

He tries, and fails, to formulate a question about the "academy" that isn't horrifically rude. Ensign Kim looks a bit old to have just finished his schooling-- and he couldn't have had time to earn his promotion. Perhaps he had a noble title? But he wasn't introduced with one. It's a puzzle, but one Laurence has no way to pry at just now.

Instead he asks "Was Voyager a highly sought-after post?"

Harry grins.

"Yeah, actually. I was valedictorian at the academy and I wasn't all that confident I'd get it."

"Valedictory... an?" Laurence asks, wretchedly.

"Oh, uh, they rank the members of each graduating class, based on their academic performance mostly. Valedictorian is, uh, 1st."

Kim is somewhat discomforted at having to spell this out.

Ah! This is starting to make more sense.

"Admirable," says Laurence approvingly, feeling a flash of warmth for Kim. "Young men who attend this academy are favored for officers generally, then?"

"It's the only way to start your career as a commissioned officer. There are field commissions, but most officers went through the academy."

"Sounds like that's a bit different from how they did things in your time?"

"Remarkable that so many have the funds to enroll." To Laurence, an academy is primarily a place for indolent gentlemen to amuse themselves discussing philosophy. But he supposes this one must be different, if it's considered an appropriate preparation to be an officer. "My own schooling ended when I left home for the Navy, though the better captains will set their boys to sums and trigonometry. I learned enough to be going on with on board ship."

"Oh, we don't use money, generally. Anybody can go to the academy if they pass the entrance exam."