This webpage at Spouses.nu provides useful information for those willing to learn Swedish in Stockholm.
Personally, I recommend learning Swedish by Rosetta Stone (linked to their UK website), especially if you are too busy to go to a language school. Download the demo software to see how it works. It's not purchasable in Sweden, though (as far as I know). Order it at your own country's website if you are from US, UK, France, Germany, Italy, Japan, or Korea and ask your family or friend to send it to you.
To learn the Swedish grammar, Essential Swedish Grammar by Julian Granberry (New York: Dover Publications, 1991) seems to be the best affordable textbook (buy one at amazon.co.uk).
A Swedish native speaker teacher has started blogging about the Swedish language since February 2010. Check this out.