Bromma airport to Stockholm

The Bromma airport website lists the transportation option.
http://www.brommaairport.se/en/Bromma/Traveller/Getting-to-and-from-the-airport/Buses/ The cheapest way is to take the local bus (SL) from the airport. If I were doing this, I would probably choose the 110 bus to Alvik where you could then switch to the tunnelbana (green line) which will take you into central Stockholm. If you are staying in Stockkholm, you could buy either a 24 hour or 72 hour card which would cover this trip plus any other trips you make on bus or t-bana in Stockholm. You can buy the ticket at the news stand called Pressbyrån in the airport. The most direct way is by flygbus. Most people find this easier than public transportation. This costs a lot more than the local bus. This bus goes to Stockholms Cityterminalen which is across the street from the Central Station where you can catch the tunnelbana to other locations in Stockholm. You can also consider a taxi.

Forgot to mention we will be flying in at 9:30 in the evening. but I will look at the website and see the options. Thanks

At 9:30 pm, I'd probably choose the flygbus over the SL bus. The SL bus/tunnelbana would be perfectly safe, but it will take longer and likely run less frequently. How many people are you? Bromma is the closest airport; a taxi will probably be 300 SEK or so. Depending on how many you are, that might not cost much more than the flygbus.

There are five. Two adults, 2 young adults, one chlid