I'm going to have my PCs pulled out of hyperspace by an Interdictor that is running smuggler patrol duty on a hyperlane. The captain is going to be an amicable fellow and offer the PCs a lift to their destination (since their patrol is over and they just so happen to be going that way)

Well, what could the PCs reasonably do while aboard, after they are shown to their room?

So awesome! In our June session, my players were given coordinates to meet a collector of rare items who could buy the Jedi artifacts they found in temple ruins.

It turned out to be a Rear Admiral aboard an Immobilizer 418 cruiser.

The Admiral was amicable, I suppose - he bought their artifacts and allowed them to leave. Someone they were travelling with had other plans, though and decided to sneak around the ship, steal information and fleet positions, and then they all had to fight their way out and escape. They went into hyperspace 15 feet below the hangar to avoid TIE Fighters and tractor beams.

The Immobilizer is likely my favourite Star Wars ship. I dunno I just love the bubbles!

The nature of their visit is entirely different than in your example. Perhaps they could spend time in the rec room conversing with troopers and officers? They could get tours of the equipment, ships, and walkers (not sure if they have walkers). They might also spend time in astrogation I guess or have tea with the Captain in her quarters.

I don't imagine the Imperial ships are very fun.

Warships tend to be very spartan and with plenty of no go areas. Probably not many places or really any without an escort.

I'm going to have my PCs pulled out of hyperspace by an Interdictor that is running smuggler patrol duty on a hyperlane. The captain is going to be an amicable fellow and offer the PCs a lift to their destination (since their patrol is over and they just so happen to be going that way)

Well, what could the PCs reasonably do while aboard, after they are shown to their room?

Drink and play sabbac with the off-duty crewmembers, flirt with the captain, be falsely accused of a murder that happened in the middle of the night with no witnesses, help man the guns during a rebel ambush ("What do you mean you don't want to? They're firing at us!"), cook a meal from their home planet to break up the bland routine canteen food that the non-officers have to eat, be made to paint the hull for flirting with the captain, search for the missing ship's mascott (a nexus called Burper who is tame only for the chef who feeds it), take up all the floors trying to retrieve the Force-sensitive's lightsabre that rolled down through a grill without alerting any of the Imperials what you're doing or what you're looking for.

Hope that gets you started. Lots of fun to be had aboard a Star Destroyer.

Given a tour, Bridge, Hanger, Training rooms, and maybe even engineering

Taken to the simulators (allows everyone to safely enjoy fighter combat without DYING)

You could visit the canteen.. Google the Eddie Izzard Death Star Canteen sketch 7:53 mins sketch

*video removed - language!!!*