Stockholm hotel and sights for two full days

My wife and I are hoping to visit Stockholm next week (we fly standby, so we have to wait and see!).

Not sure what your definition of "boutique" might be, but we have a list of 5 possible hotels for us. Top of the list is Hotel Skeppsholmen (https://hotelskeppsholmen.se/en/). It's a bit pricier, but it gets a pretty good rating on many sites. Plus, it is right in the middle between the Royal Palace, Vasa Museum and Skansen open-air museum. Looking at the tourist maps, there's a water taxi (or whatever you call it) stop right nearby.

there's a water taxi (or whatever you call it)

It's called a ferry.

Skeppsholmen is certainly a nice area to stay in, but it is not that central as it is only connected by one bridge and the ferry. So if you are looking for easy access to the rest of the city, it might not be the best location.

We stayed on Djurgarden, easy access of island by ferry and bridge. Many museums are there.

I stayed in Hotel Sven Vintappare, which is in Gamla Stan. It’s not downtown, but it’s easy to get to the main sights, and Gamla Stan is charming and beautiful. The hotel - really a small B& B - is in a super old building (like 1600s) and is full of character and very Swedish. I just loved it. Because of the age of the building, it has quirks like narrow staircases (I don’t think there is an elevator) and sloping floors. The bathroom was small, but our room was huge. We enjoyed our breakfast, and the staff was excellent. It’s been a while since we stayed there, so you might want to check recent reviews on Booking.com or Trip Advisor.

Don't click on the link in hamandaxen's post. I've reported it.