I can spend one day in Oslo early September. I am wondering how is the weather in Oslo in September and where I can visit with having 12 hours, from 8 am which I land at the airport to 8 pm.
Many years since I was in Oslo but some things I do remember:
The Vigeland park - with sculptures of Vigeland, nice place to spend an hour or two, though if you will enjoy the sculptures I don't know, they were not quite my taste
Akershus fortress - old castle with the normal "castle things"
the most intereseting may be the Viking ship musuem, it is a short distance from the centre.
The weather will be unpredictable, could be raining, or sunshine. Temperatures around 10-20 degrees but probably at the lower end.
My favorite things were the Fram museum, the Kon Tiki museum and the viking ship museum (I love all things related to the sea and exploration.) The castle was also fun to explore.
I'm paraphrasing for Scott, who lived in Oslo very recently:
Oslo is VERY expensive, it costs quite a bit to catch the train out of the airport, cheapest thing to do would be to get a day pass for the metro. The art museum (outside of it) is very cool (you can walk on the roof), The kings castle, Vigeland park is really cool. He says that just walking around the city is quite nice (and cheap)
The weather in Sept is quite cool, they start to get snow in October so make sure you bring some layers! (jacket and sweater)
Also, you should visit "Bjørvika" and the new opera there. If it's raining it may not be the best thing to do, but if the weather is sunny there are always a lot of people sitting on the roof relaxing.