Sorry for the huuuuuuge delay in replying to you. I've not been around for ages due to work/personal stuff
Firstly, welcome to BE
As to your query, i admit to not being overly surprised that you've fallen in love with Göteborg and Stockholm - most people who ever visit them do fall for them more or less straight away!
I agree that Stockholm is certainly the most beautiful of them, especially in the middle of winter and middle of summer, although Stockholmers can have a sort of superior attitude to other lowly people... Göteborg has always been more cosmopolitan and friendly, partly because of the large industrial areas, but mainly because of the huge dock and shipbuilding histories, although they are both in decline now unfortortunatley.
As to getting a decent job with little or no Swedish, it is possible but there is a lot of competition. You can almost always get basic work (teaching, bar/entertainment etc) with no Swedish whatsoever, but for "proper" jobs your best bet is if you have some sort of specialist background/experience/knowledge, even if you are looking at managment positions. There are lots of managment jobs, but also lots of applicants, and for most average Swedish management jobs, unless you have a certain something which takes you above the (for want of a better term) average candidate, the chances are they will take somebody who speaks Swedish in preference.
However, there are lots of companies/positions where English speaking is valued allot higher than Swedish, and at least half of all job adverts in management etc will be written in English instead of Swedish anyway. Whilst virtually Swedes speak scarily impressive English, sometimes in business they like having a native speaker to liase or at least be first contact with international clients. They are also accutely aware that English is the international language of business, so take any opportunity to practice their English, especially with native speakers. Again, some sort of specialist expertise/background would help, but i'd suggest aiming for either international firms with Swedish offices/branches etc, or Swedish firms with international standing and who will use lots of English for documents etc and communicating with the different offices.
I would also suggest that maybe smaller companies who are looking to exapnd into other markets/areas often offer a better chance for non Speakers than larger such as Volvo or Ikea - yes they have lots of positions, many of which you need no or little Swedish, but they are also the sort of comapnies that are liable to get flooded with applicants, and often will even recruit in places like the UK or US anyway. Smaller companies looking to expand abroad and looking for native English speakers or with international experience/qualifications/skills etc are often more likely to choose a non Swedish speaker. And most comanies - large or small - are very happy to subsidise or pay for Swedish lessonsfor you anyway.
I'm not entirely sure how helpful any of that really is, but hopefully there's some bits of interest there. If you've got any questions/want to chuck ideas at someone/are looking for more information, just let me know.
And again, my apologies for the delay.