36 hours in Oslo

I have been to Oslo several times but near heard of Smøgen--- because it is in Sweden. Why not stay in Oslo and visit the museum island with the three ships museums---- old Viking ships, modern Norwegian explorers, and Thor Heyerdahl?

http://www.visitoslo.com/en/activities-and-attractions/boroughs/bygdoy/

I also loved Oslo--so much to see and do there. We enjoyed our visit to the Royal Palace and Ibsen's home which is very near the palace. Several other highlights to choose from were the gorgeous City Hall where the Nobel Prizes are awarded, Vigeland Park filled with the artist's sculptures, Akershus Fortress, the Viking Boat Museum, the National Gallery which houses Munch's "Scream," Grieg's House, and Ole Bull's home which you access by boat.

On first reading I had assumed that OPs must have visited Oslo one or more times in the past. Why else would they leave town if they only have a day plus to enjoy Oslo?

One would have to run through the Rick Steves highlight list to do a "check off" tour in 36 hours given that they are not open at night:

https://www.ricksteves.com/europe/norway/oslo

At a Glance
▲▲▲ City Hall Oslo's artsy 20th-century government building, lined with huge, vibrant, municipal-themed murals, best visited with included tour.
▲▲▲ National Gallery Norway's cultural and natural essence, captured on canvas.
▲▲▲ Frogner Park Sprawling park with works by Norway's greatest sculptor, Gustav Vigeland, and the studio where he created them (now a museum).
▲▲▲ Norwegian Folk Museum Norway condensed into 150 historic buildings in a large open-air park.
▲▲ Norwegian Resistance Museum Gripping look at Norway's tumultuous WWII experience.
▲▲ Viking Ship Museum An impressive trio of ninth-century Viking ships, with exhibits on the people who built them.
▲▲ Fram Museum Captivating exhibit on the Arctic exploration ship.
▲▲ Kon-Tiki Museum Adventures of primitive Kon-Tiki and Ra II ships built by Thor Heyerdahl.
▲▲ Holmenkollen Ski Jump and Ski Museum Dizzying vista and a schuss through skiing history.
▲ Nobel Peace Center Exhibit celebrating the ideals of the Nobel Peace Prize and the lives of those who have won it.
▲ Opera House Stunning performance center that's helping revitalize the harborfront.
▲ Akershus Fortress Complex and Tours Historic military base and fortified old center, with guided tours, a ho-hum castle interior, and a couple of museums (including the excellent Norwegian Resistance Museum, listed above).
▲ Norwegian Holocaust Center High-tech walk through rise of anti-Semitism, the Holocaust in Norway, and racism today.
▲ Norwegian Maritime Museum Dusty cruise through Norway's rich seafaring heritage.
▲ Edvard Munch Museum Works of Norway's famous Expressionistic painter.
▲ Grünerløkka Oslo's bohemian district, with bustling cafés and pubs.

I was in Oslo this past May and took a day trip to Fredrikstad. It was a drizzly Monday, and the town was very sleepy. I understand it is a hugely popular weekend getaway in the summer. I have no idea what it might be like in September. It's just over an hour by train from Oslo, and the trains run once per hour. I think it could be a good option for you, assuming you have previously spent time in Oslo and feel that you've seen all you're interested in seeing there.

Thank you to everyone for your advice. We were thinking that after being in Copenhagen for a few days we would be ready to get out of the city scene and would take the opportunity to see the famed Norwegian countryside. Maybe we will stick to the city sights instead.

If you buy an Oslo Pass, the one day pass is actually a 24 hour pass that starts when you validate the pass. If you validate the pass at 11:30 of the 22nd, it would be good until 11:30 of the 23rd.

http://www.visitoslo.com/en/activities-and-attractions/oslo-pass/

http://www.visitoslo.com/en/activities-and-attractions/attractions/

I'd also vote for staying in Oslo! We just got back, and it's a beautiful city. The Oslo Pass saved us money, so I'd crunch numbers before you go - it might be worth it for you, too. The highlights for us were (grouped by location and listed in order of preference):
-Munch Museum and Botanical Gardens (if you're staying in the city center, you'll need to take a bus or tram, included in Oslo Pass)
-Norsk Folk Museum, Viking Ship Museum, and Flam Museum (if you're staying in the city center, you'll need to take a bus or ferry, included in Oslo Pass)
-Akerhaus and Resistance Museum (close enough to the city center that you should be able to walk from most accommodations)

I would include a visit to Holmenkollen - the skiing museum - and to Vigeland (http://www.vigeland.museum.no/en/vigeland-park)

T-Bane ride to the Holmenkollen skiing museum/jump tower and Vigeland park are my repeat visit favorites. The Holmenkollen jumping tower (and the T-Bane ride to Holmenkollen offer scenic vistas of Oslo and its fjord with the jumping tower a spectacular observation point of the City and the surrounding forest. The Vigeland park is a pleasant stroll and viewing the sculptures in their outdoor setting is worth repeat visits.

I just returned from a road trip from Bergen to Andalsnes to Oslo. I stayed one night in Lillehammer on the way back to Oslo. If one is passing through Lillehammer, the Maihaugen open-air museum is well worth visiting, especially if the weather is nice. On the other hand, I am not sure it's worth making a trip from Oslo to see that museum, especially given the fact that there is a similar (possibly larger) museum in Oslo, namely the Norsk Folkmuseum (which I did not visit). As others have said, Oslo is a very nice town and there was plenty to keep me busy in the 2 1/4 days I was there. If I had a third day, and hadn't been to Lillehammer, I probably would have spent it at the Folkmuseum. I understand there are other interesting towns near Oslo that may be worth a day trip, but I am not sure it is worth going out of your way to visit Lillehammer unless there is something specific you would like to see there.