The local transport authority has a good travel planner, allowing you to type in prefered times of departure/arrival, etc. For example, getting to Hötorget (the underground closest to SIF, I think) from Åbyvägen 20 tomorrow morning, with a departure around 8.15am: reseplanerare.sl.se/bin/query.exe/en… . Play with the times to suit your required travel times and be sure to check destination and route maps so you know where you're going.
Your hotel actually has very detailed info about alternatives on their web page, but I can only find it in Swedish. Don't hesitate to mail them and chastise them about this, asking for travel information in English. It may be an oversight on their part, or they may already have an information sheet they can mail to you.
The same travel planner can be used for your trip from the airport, though you should take the airport coach or Arlanda Express to T-Centralen, starting your public transport search from there to Åbyvägen.