Akershus Fort and Castle was nice to stroll through, if the weather is nice. The Nobel Peace Center, City Hall too.

http://www.visitoslo.com/en/activities-and-attractions/10-suggestions/

We ate at a lovely cafe near the Castle, with outdoors tables [it was very warm last April]. Lots of great spots along the water/harbor.

Hot Club de Norvège concert at Soria Moria Kulturslott tonight Friday at 8pm: http://www.visitoslo.com/en/whats-on/events/?TLp=655063&Hot-Club-de-Norvege-Touche-=

Fabulous Valkyrien Allstars concert tonight at 9pm: http://www.visitoslo.com/en/whats-on/events/?TLp=646248&ValkYrien-Allstars-Danjal=

Both concerts are highly recommended, top Norwegian artists in different genres.

Saturday:
Guided tour of the new Opera house in english at 2pm: http://www.visitoslo.com/en/whats-on/events/?TLp=317997&Guided-tour-of-the-Opera-House-No-=

Cinderella at The Norwegian Opera and Ballett at 6pm: http://www.visitoslo.com/en/whats-on/events/?TLp=632337&Ballet-Cinderella=

Sunday:
Weekend walk of Old and new Oslo at 2pm: http://www.visitoslo.com/en/whats-on/events/?TLp=647507&Weekend-Walk-No-Eng-Kristiania-Oslo=

Open Day at the Royal Farm at Bygdøy from 11am to 4pm:
http://www.visitoslo.com/en/whats-on/events/?TLp=653576&Open-DaY-at-the-RoYal-Farm-BYgdo=

Much more on "What's on in Oslo": http://www.visitoslo.com/en/whats-on/events/

Restaurants/bars with atmosphere:
Perhaps traditional Norwegian at newly renovated Olympen from 1892: http://www.olympen.no/olympen

Lorry just behind the Royal Palace is an institution in town and high spirited: http://www.lorry.no/

Lunch at Theatercaféen: http://www.hotelcontinental.no/Default.aspx?ID=236

Laid-back atmosphere and fine food in Café Laundromat, next to Bislett arena: http://www.laundromat.no/

Lots of vibrant places in Hegdehaugsveien and Bogstadveien between the Royal Palace and Majorstuen. http://www.visitoslo.com/en/activities-and-attractions/boroughs/oslo-west/

Lots of great restaurants and bars and the best atmosphere in casual Grünerløkka: http://use-it.unginfo.oslo.no/WP/nightlife/grunerl%C3%B8kka/

thanks -- this was so helpful! am saving these links for anyone else going there too

You've got lots of good suggestions, but Vigeland/Frogner Park is my favorite spot in Oslo.

You could also take the quick ferry ride to the open-air Norwegian Folk Museum to see a collection of homes from as far back as the 1200's, and a Stave church -- all in a beautiful setting. They also have folk music concerts. Really enjoyed it.

Frogner Park with it's wonderful sculptures, Viking Ship Museum,Folk Museum, new Opera House where you can walk on the "roof." Lunch on the Ackker Brygge at Lofoten; order the big bucket of shrimp.