Some of the main Oslo sights and attractions:

 

BYGDOY PENINSULA

(Have bus no. 30 to Museum of Culture History, walk next door for the Viking Ships, bus to end stop or a 10-15 mins walk downhill to Kon-Tiki, Fram and Maritime museums; then ferry return to City Hall pier):

Museum of Culture History (Open air)

Viking Ships

Kon-Tiki (Thor Heyerdahl explorations)

Fram (Arctic explorers)

CITY CENTRE

Akershus Fortress & Castle

Resistance Museum (WW II - At Akershus)

City Hall area

City Hall

Historical Museum

Karl Johan (Main street with Royal Palace, University, National Theatre and Parliament)

Aker Brygge (Shipyard turned into a shopping mall with restaurants etc.)

Oslo Opera

OSLO EAST

Medieval park & rock carvings

Annual Medieval Festival

OSLO WEST

Vigeland Sculpture Park

Holmenkollen Ski Junp arena (being rebuilt at present; will be open next year)

OSLOFJORD

Fjord trip (incl. visit on Hovedoya - the island closest to the city with medieval ruins of monastery)

Gressholmen (neighbouring island to Hovedoya)

DAY TRIPS ON THE FJORD FROM OSLO

Oscarsborg Fortress

Drøbak (coastal village by the fjord)

 

For more inmformation about Oslo - what's on when you are visiting; info about Oslo Pass - useful if you travel by public transport and visit many museums etc.)

http://www.visitoslo.com/en/