We are taking a cruise with NCL and will disembark in Stockholm (Vartahamnen).

Since your flight departs for the USA at 8:00am the next day, I would stay at the airport. You can go ion the Arlanda Express( train) into Stockholm the night before you leave to explore it a little and then return by train again to your airport hotel.

Thanks for your reply. So to clarify, once we disembark (around 7:30am), it would make sense to travel to the airport hotel to drop off luggage and then travel back to the city center to explore and then back to the hotel to sleep the night? Any recommendations for hotels near the airport?

1. I would not recommend staying close to the port, so the question is if you should stay at the airport or in the city. You don't mention which airport or where you are flying to so I'm assuming Arlanda. 8 is early, but not extremely early. You should probably try to be at the airport between 5 and 6 depending on where you are flying to. You could either stay at the airport, it will save you a bit of time in the morning. Or you can stay in the city, in which case I'd suggest a hotel close to the central station.
2. If staying in city, at the hotel. Or if staying at the airport there are lockers at the central station.
3. It depends a bit on what you are interested in and what you want to see and do.
4. For your limited time I recommend the airport train, Arlanda Express. Takes you from the central station to the airport in 18 minutes.

The Arlanda Express is very efficient, but it’s a bit pricey. I myself would not pay three trips on it within the span of one day (I.e. if you were to go to an airport hotel, check in, come back into town, and then go back out to the airport hotel again).

You can leave your luggage in paid lockers at Central Station, where you catch the Arlanda Express.

Thank you for the information. I was unaware that luggage storage was an option at the station. That sounds like the perfect solution. We will stash the luggage and plan a semi-private tour of the city. I see one offered for Gamla stan and Stockholm Old Town. At the conclusion of the tour, we plan to travel to a hotel near ARN for the early departure. Please advise if there is something we should not miss!

Thanks for your reply.

I’ve seen 2 videos n Stockholm in the past week. Both couples visited and enjoyed the Vasa Museum and the ABBA Museum

Gamla stan is the old town and it's easy to see on your own without a tour. It's a short walk from the central station. You haven't told us anything about what you're interested in, so it's hard to give advice. But the Vasa museum is very popular (and for a good reason, it's a great museum).