Our cruise leaves from Stockholm on September 2nd. We will arrive very early on August 31st so, jet lag nothwithstanding, we should have 2 full days to explore this city. Being the short amount of time, is a tour better than DIY or can we adequately see it on our own? Aside from the Vasa Museum, what are the other must sees? Is the Stromma boat tour a good way to get an overview the first day (without falling asleep) or best saved for the second day (or even right before leaving to board the ship? Best option for transportation for 6 from the airport? Last but not least, we are booked in 2 different places right now, the Sheraton and the Marriott Courtyard, with the latter being half the cost of the former. The Courtyard seems like it might be further from all the things to see therefor justifying paying the higher price for the Sheraton if it makes it easier to get to everything. Appreciate any and all insight :)
For 6 from the airport, a taxi (or 2 taxis) is probably the best option. Taxis are not regulated in Stockholm so it is very important to use one of the reputable companies to get a fair price. Taxi 020, Taxi Kurir, and Taxi Stockholm are all reputable and will offer a fixed rate to the city. I don't know what the current fixed price is; a couple years ago it was around 500 SEK for a standard sized taxi.
The Sheraton is close to the Central Station so quite convenient. I had to look up the Marriott Courtyard; it is on Kungsholmen near a big park called Rålambshov Park which leads down to the water and often has various activities (soccer, volleyball, frisbee, etc.). It is a more suburban part of the city so you will be taking the subway (tunnelbana) or bus to most sites. It is a perfectly fine location as public transit is very good in Stockholm. It just depends on whether you mind the extra travel time. It is on the "green" line, Fridhemsplan is 5 stops from T-Centralen. You might want to buy a 24 hour or 72 hour ticket for SL so you can use the buses and underground freely.
I'd check the weather on arrival before you commit to a day for your boat trip.
Besides the Vasa Museum, take one of the outstanding tours of the City Hall ( Stadshuset). Wander through Gamla Stan. Visit Skansen.