Re: Stockholm to Nynashamn
3 hours might be tight depending on if the flight is on time or not, if you've checked in baggage or if you come from an EU or non EU country (if you have to go through passport control or not).
To go to Nynäshamn you have the following options (ranked from the fastest to the slowest):
(1) Arlanda Express train to Stockholm's central station and then commuter train to Västerhaninge and then bus to Nynäshamn
(2) Bus shuttle (flygbussarna) to Stockholm's central station and then commuter train to Västerhaninge and then bus to Nynäshamn.
Normally there's a train going straight to Nynäshamn but they're doing works on that line, which is why I wrote "train to Västerhaninge and then bus to Nynäshamn".
I don't recommend going via Märsta because it takes longest. You could also take a taxi if you have a lot of or heavy baggage but that will cost you a LOT.
The Arlanda Express ticket costs 220 SEK (adult, no discounts) but the train takes 18-20 minutes. The bus shuttle costs 90 SEK, and then the SL ticket to Västerhaninge/Nynäshamn costs between 60 SEK.
Arlanda Express: http://www.arlandaexpress.se/
SL (commuter train and bus): sl.se/Templates/SubStart.asp...
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