Of course, since JerseyGirl actually lives there, she knows better than anyone, but I'll put my two cents in on my experiences as a tourist:
ArtMan, in terms of the weather, I agree that it was jacket-cool rather than actually cold. I went the last week in May and the first week of June of 2013. I brought a winter coat but didn't wear it once. It was probably similar to New York in early April. Maybe in the 50s or even low 60s during the day. It rained some, but I was there for over 2 weeks so that's going to happen. Looking online, it says there's precipitation about a third of all days, which is about the same as in New York.
In May, the sun also stays out late in Stockholm and Oslo - sunset isn't until almost 10pm. So from a tourist perspective, it's light out even at night and it feels safer (it's extremely safe, anyway).
Ironically, the warmest part of my trip was in the Arctic Circle. It was over 70 degrees up there. But they also told me that the previous year at the same time, it was snowing, so I guess the weather up there is very variable.
I wouldn't take a trip to Sweden that includes Gothenburg but not Stockholm, unless you think you're going back again. Gothenburg is fine, but from a tourist perspective, there's not that much. Stockholm is where it's at in Sweden for tourists. It would be like taking a tourist trip to England and never going to London.
FOAnatic, you should of course do the things that you're the most interested in rather than the things that other people tell you to do, but if you're going to be in Norway, I personally wouldn't miss a chance to see the fjords, and if you're going to see the fjords, I would do the Norway in a Nutshell trip because it's the most straightforward way of doing it. It's a big tourist thing, and if you google it, there are clear directions about how to do it one day. I think it's also in one of the Rick Steves books. It takes the whole day (the outgoing train is at something like 8am and you come back at 11pm) but it's definitely worth it. It's not very tiring because you spend most of the day sitting on a train or a boat, looking at incredible scenery.
"What was the name of that cheese that I like?"
"you can't run away forever...but there's nothing wrong with getting a good head start"
"well I hope and I pray, that maybe someday, you'll walk in the room with my heart"