Instead of getting a taxi for approx €60 or taking the Arlanda Express for approx €20-30, I'd recommend using the far cheaper public transport option.
There's a frequent bus from the terminal to a nearby station and a very pleasant train ride into the city centre.
The info desk in the airport are also very helpful and will point you in the right direction.
Google map: bit.ly/L7A0Nq
In summer consider renting a public bicycle. The cost of three days is 125 kr (or 250 kr for the whole season). You can get the card to use the bikes at any SL centre. You can use a Bicycle for three hours, then place it back in one of the 70 stations in Stockholm, and you can grab another one.
It's available from 6am to 6pm every day.
I strongly recommend a little extra time when planning your transport time in the summer months. Most Swedes take all 5-6 weeks of vacation in one stint in July or August so buses and train schedules are greatly adjusted for what staff there are.
The Arlanda Express is a fast train service from the airport to Stockholm city centre. Although it is quite expensive, around £12 one way, it covers the 40km to the city in 20 minutes.
Tickets can be bought from easy-to-use machines. The airport itself is modern, clean and well-organised.
Arlanda Airport is the main connection for Stockholm.
Absolutely fabulous! In the archipelago outside Stockholm you can either take a trip in a boat of your own, take a daytrip with Waxholmsbolaget for example or cruise around ("båtluffa") for a few days.
Easily reached by train, this beautiful seaside suburb south of Stockholm is an ideal place to visit for a day trip from the Swedish capital. The small sandy Baltic beaches are ideal for children and there are old-fashioned separate male and female nude swimming areas and saunas. You can go for walks in the woods, picking berries and mushrooms, or try one of the bars and fish restaurants.
Take the historic train ride from Slussen station in Stockholm to Saltsjöbaden.
The easiest way to get around in Stockholm is to buy an SL travel card which provides unlimited travel on all tubes and buses (and even some boats!). A 3-day card costs approximately £13 and 7 days' travel will set you back about £16.
This card is excellent value for money. You get a discount on hotel rooms plus access to any public transport, to most of the museums and even to some of the boat trips on offer. You don't have to worry about tickets, which makes your stay much more relaxed. The hotels on offer suit any of your needs – ranging from two to five stars.
A boat trip out to the archipelago is a fantasic day trip if you're here for a few days. The trip alone is great fun, on board old-fashioned steam boats, but the islands are stunning. You will have whole meadows, sandy coves and rocks to bask on all to yourself, and if you’re brave the water’s cold but invigorating. Grinda is a lovely small island, with the trip taking about an hour and stopping at Vaxholm on the way there and back.
The ferries crossing the sea between Stockholm and Helsinki are notorius for on-board alcohol-induced shenanigans. It takes about 12 hours from Stockholm to Finland and most passengers opt for a Nordic buffet with a disco and a lot of booze afterwards. The ferry terminals are very close to Helsinki city centre, which makes the ferries convenient for a day trip. That is, if you can get out of bed the next morning.
Gardet subway station is 500 metres from the ferry terminal or there is a bus which connects the ferry terminal with the City Terminal, near the main railway station.
Stockholm Vartan terminal, Sodra Hamnvagen 46.
Aside from the normal try: the Stadsbiblioteket (national library) on Odengaten. Designed by Gunnar Asplund in 1924-8 a stunning series of spaces lovingly used and preserved. The same architect designed the Southern Cemetery (Skogskyrkogården with metro stop of same name): the chapels are in use so access is difficult although the landscaped grounds are beautiful and reflective.
Asplund worked with Sigurd Lewerentz on the cemetery: the latter designed one his two great churches in southern Stockholm: Markuskyrkan at Bjorkhagen (1958-60): one of the great post war buildings.
If you liked the dark brick modernist space of Markuskyrkan then try Celsing's St Tomas kyrka at Vällingby (1951). Both these churches are right by the suburban metro stops.
For the first two days we bought a 'Stockholm card', which gave us admission to loads of museums and attractions as well as unlimited travel on buses, metro and regional trains. We stopped at a hotel just out of the city centre and travelled in every day, the buses and trains always run to time and getting around is very easy.
We flew from Heathrow to Arlanda airport and then caught the Arlanda express into the city. This was fantastic - fast, clean, on time with the politest staff ever!
Following on the comment about not going at midsummer, watch out for the Scandinavian saturday - not so much of a big deal in Stockholm, but shops close early (from midday onwards), public transport links are worse than any other day and pack up early, and concerts are often held in the afternoon not evening. All good locals obviously go off to be with the family.
This maritime-themed boutique hotel is chic, has fabulously comfortable beds and is suitcase-dragging distance from the railway station. It also has its own ice bar, where you can don yeti-style fur coats and slurp back vodka from ice glasses. The restaurant serves up a mean rhubarb pie, too.
Nordic Sea Hotel Stockholm
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