Abisko is a great place to see aurora! There are two nice little ski resorts nearby. Family-friendly Björkliden is about 10 km from Abisko, and Riksgränsen (my favourite of the two) is about 35 km away - but Riksgränsen most likely won't be open in December. Abisko itself is great for cross-country skiing.
Some more info about aurora in Abisko: http://www.auroraskystation.se/
http://www.abisko.nu/vinter/englishpages/index.asp

If you decide to go to Abisko you can stop in Kiruna on the way (100 km from Abisko) and visit the Ice Hotel in the village Jukkasjärvi. This is another good spot to see aurora since Jukkasjärvi generally has many clear and cold - very cold! - vinter days.