Hope I'm not too late for my two cents!
food - my favourite restaurant I visited was a Vietnamese place called Nem Nem Quan in Söder (an island south of the city). I didn't press them too much on the veganess of their vegetable dishes, but I had a delicious vegetable curry. It's very popular so you'd probably have to call and book ahead. I find that Söder in general is a haven of health food shops and restaurants. There is also a vegetarian/vegan cafe in Söderhallarna (http://www.soderhallarna.com/english
) called Södermanna (http://sodermanna.se/meny.html
) sorry it's in Swedish, but I'm sure google translate can help! They have wraps, falafel, vegan kebabs and the like. My omni otherhalf loved their vegan kebab plate! Söderhallarna also has an english shop! (maybe not so interesting for you, but being an expat Brit, I have to stock up on my tea there!)
Hötorgshallen (the old haymarket; http://www.visitstockholm.com/en/Dine/R ... allen/1060
) is more central, also a great place to check out, not so much for being overly vegan friendly, but it's a great food market to look around and the coffee bar there (himalayan something or other) is amazing - had the best flat white of my life there! You can also laugh at all the people queueing for over the counter service at Systembolaget (state run monopoly alcohol shop) - apparently all the alcohol used to be bought like this, with the alcohol tucked safely behind glass and staff!
Sightseeing - nordiska museet (Nordic museum) is a beautiful building just to see from the outside, but I enjoyed inside too. The Hallwyl museum is close to the nordiska; it's a palace that is preserved from a hundred years ago and I really loved the tour (available in english), but I'm a nerd :D
It's been a bit longer since I visited Gothenburg, so my details are a little more sketchy - all I really remember is that they have a medical museum that I really enjoyed (complete with a little english booklet as the displays are mostly in Swedish).
As someone above said, fika is serious business, and you should partake! As are saunas (bastu) and you should definitely do one! Have fun!
*edit to add more links