Birthday weekend in Stockholm - need ideas!

We'd like to get a family room in a quite nice, small hotel (ideally a
great value "luxury" boutique hotel) in the part of town that is the
most walkable to the stuff we'd most want to see during a first visit.
Would this be Gamla Stan? Any hotel recs?

It's hard to say without knowing what you want to see. But for some nice and small, book the captain's cabin on Af Chapman. https://www.swedishtouristassociation.com/facilities/stf-stockholmaf-chapman-skeppsholmen-hostel-house/ Not the best location, but not the worst either. Assuming the ship is not closed for renovation during your trip.

Any not to miss sights/experiences for a quick first trip?

What are you interested in? What do you want to see and do?

We will be taking the ferry to/from Helsinki and will have two
almost-full days in Stockholm (overnight ferry/one night
hotel/overnight ferry). However, we would consider flying one
direction if cost-effective and doing 2 nights in a hotel. If so, we
think the return would be best on ferry to see the archipelago at
sunset?

Flying will not be cost-effective. The ferries can be ridiculously cheap and are in general a much nicer experience than airport queues.

Any tips for booking cabins on the Silja line? Is a sea view cabin
worth it? Is the buffet worth it?

Avoid the cheapest ones (C). Sea view is worth it if you want the views, but I'd recommend a cabin with a window towards the outside. Regarding the buffet, could be a good option but the ferries usually have many options for dining. It seems like Silja line doesn't publish the buffet menu online, but Viking line does and I assume Silja's buffet won't be too different. https://www.vikingline.se/globalassets/documents/menus/the-buffet/the-buffet_010922-x_amorella-gabriella-glory-grace_en.pdf

Would this be Gamla Stan? Any hotel recs?

I’d also look at hotels in Östermalm or Södermalm in addition to Gamla Stan. In general, Stockholm is very walkable and well served by public transportation so you don’t need to limit yourself just to the old town. Unfortunately, I don’t have any specific recommendations. I stayed at af Chapman in the early 90s. It is a hostel and interesting experience but it sounds like you want a boutique hotel.

Any not to miss sights/experiences for a quick first trip?

For me, I think the top sites are the Vasa Museum, a tour of the City Hall (Stadhuset), and a walk through Gamla Stan. When I was living in Stockholm, these are the places I always sent guests to see.

We will be taking the ferry to/from Helsinki and will have two almost-full days in Stockholm (overnight ferry/one night hotel/overnight ferry). However, we would consider flying one direction if cost-effective and doing 2 nights in a hotel. If so, we think the return would be best on ferry to see the archipelago at sunset? Any tips for booking cabins on the Silja line? Is a sea view cabin worth it?
Is the buffet worth it?

I wouldn’t fly as the ferry is a good value and much more pleasant than flying. It is nice to get a cabin with an outside window, but not necessary. I am not a fan of the buffet, but some people like the buffet to get a sampling of various Scandinavian specialties. There are some very good restaurants on the ferries and I prefer to go to one of the restauants with an a la carte menu. You can book some of the restaurants in advance and they may let you book a table by a window.

For a special date night dinner in Stockholm - we are looking for a small, classy, pretty and intimate place full of locals :) dpesnt have to be necessarily walkable from the hotel. any recommendations?

You will have lots of choices; your hotel might be able to give you a suggestion. Rolf’s Kök comes to mind, but I haven’t eaten there in many years so I’d look for recent online recommendations or check a website like Eater or Michelin.

I stayed at af Chapman in the early 90s. It is a hostel and
interesting experience but it sounds like you want a boutique hotel.

Yes, they are a hostel. But they have a wide range of options, from single beds in a large room to the captain's cabin. And if you book one of the fancier rooms on the ship it will IMHO feel like a boutique hotel, even if the label says hostel.

For a special date night dinner in Stockholm - we are looking for a
small, classy, pretty and intimate place full of locals :) dpesnt have
to be necessarily walkable from the hotel. any recommendations?

What price range are you looking at? Two classical restaurants in Stockholm I'd suggest are Operakällaren and Den Gyldene Freden.

The Slussen area of Sodermalm (near Gamla Stan) is currently a major construction zone. In addition to limits on horizontal movement (which are temporary), you have the issue of different vertical levels to deal with, because the island is quite hilly You have to pay close attention to your map, because streets can end and turn into stairs, and occasionally the stairs may be inaccesible due to construction. I don't doubt that the area around Slussen is less confusing than it seemed to me today, but with only two days in the city, you'd have limited time to figure it out.

At the moment I wouldn't plan to walk from Sodermalm to Gamla Stan or any island to the north, and I'd be very careful about a hotel's walking distance from usable public transportation. I think it would be possible to end up with a not-short, hilly walk from a Sodermalm hotel to the nearest T-bana station or bus stop. Sodermalm seems like nice wandering-around territory, and it obviously has a lot of good restaurant options, but the sights listed in your guidebook will mostly be on other islands.

Gamla Stan is very, very touristy--especially when a large cruise ship is in port--but most of the foot traffic seems concentrated on Osterlanggatan, Vasterlanggatan and a few busy squares. Perhaps you'll find hotel options on other streets. Many little streets have almost no foot traffic. There's only one T station (in the SW), but there are buses running around the perimeter of the island, which is much, much smaller than Sodermalm. There are also useful public boats to some other islands with mutiple museums.

I have great doubt about the practicality of this approach on a short trip, but from my hotel on the eastern edge of Gamla Stan I have done extensive sightseeing entirely on foot in many different parts of the city: Gamla Stan itself, Skeppsholmen, Riddarholmen, Ostermalm, Vasastan, Normalm and even Djurgarden. For your purposes, though, I'd recommend figuring out your top 3 or 4 sights and choosing your hotel based in proximity to them and, if necessary, ease of public transportation.

I don't doubt that the area around Slussen is less confusing than it
seemed to me today

I wouldn't bet on it…