In reply to Cthulhu:
I live 2hrs from Åre (Biggest resort in Scandinavia I think) and Oppdal (Biggest resort in Norway) and was here all last winter and have skied at both. I love it here, but I go touring and mainly ski off-piste.
If you're really set on going to Scandinavia, then Åre is the best for your needs (You'll want to avoid this club and it's surrounds: http://www.bygget.se/ - I loved it though ;-) ). Don't go to Oppdal, it won't suit your needs.
You'll need to be lucky to see the Northern lights, I only saw them 2 times last winter, although once was while driving home from Åre.
Here's a reasonable review: http://www.telegraph.co.uk/travel/snowandski/7241887/Skiing-Is-re-in-Sweden-one-of-the-worlds-top-10...
But last season wasn't great and the mountains were fairly windswept, with the upper lifts often closed. I also found the reds and blacks hardpacked due to the wind, so not pleasant skiing; Having said that it's quite sheltered in the trees, and you could have a play on the off-piste as it's much easier to ski if the pistes are worn. The beginner slopes are very pleasant, and there's plenty of nice on-piste restaurants.
In reply to Cthulhu: The best northern Finnish resorts are Ylläs and Levi - they are not huge by Alpine standards but have a fair number of runs, plus huge amounts of quality XC tracks and opportunities to snow mobile, dog sled, reindeer rides, snow shoe etc etc if you don't want to ski everyday. The runs would be very family friendly I would think. Lots of beginner stuff and all the instructors will speak good English I'm sure - most people do here. I think Ylläs is a bit bigger, but Levi has the world cup run so has steeper stuff. A mate who is a good skier took his family to Ruka - and said it was brilliant for a family. I've skied there and thought it was too small to be fantastic, but Matt reckoned it worked well with his kids.
I don't think anything in Finland is ever particularly rowdy unless you go to the bars late at night. You would have a good chance of seeing the Northern Lights if you go mid winter. The days are quite long by Easter, so you don't get so much chance. Further north there is Riksgransen on the Swedish/Norwegian border - that has a good rep with hardcore skiers for back country stuff, but may well be OK for beginners as well. They don't seem to open until Feb. I guess because of dark and cold. The Finnish resorts have plenty of lit runs so you can still ski once its dark, that being mid afternoon around New Year.