Oslo... well, I live here. Obvious choices would include:
The Vigeland sculpture park, near Frogner. Tram 12 stops right outside, or you can take the metro or a bus to Majorstuen and a short walk.
http://www.pbase.com/ssanneru/vigelandsparken
The Holmenkollen ski-jump. Line 1 on the metro. Shame to say, I've never been there myself... I am not a winter person at all.
The medieval Akershus fortress, downtown right by the harbour. Tram 12 stops the closest I think. But it's not a big deal, down-town is quite compact.
http://www.pbase.com/ssanneru/akershusfestning200902
The Viking Ship museum or the polar ship Fram museum, both on Bygdøy right outside town and reachable by bus 30.
http://www.pbase.com/ssanneru/the_viking_ship_museum
There is also the National Museum, next door to the Viking Ship museum, where you can photograph various preserved historical buildings if you so want, including a geniuine medieval wooden Viking-style "stave church".
http://www.pbase.com/ssanneru/oslofolkemuseum201003
http://www.pbase.com/ssanneru/norskfolkemuseum
The brand spanking new Opera House, it is quite picturesque (do bring a serious wide-angle) and is on the seaside right next to the main railway station.
http://www.pbase.com/ssanneru/operahuset
I am certain that others will pipe up with more out-of-the-way suggestions in due time. The weather here is nicely springlike at the moment but that is not to be taken for granted. Do bring good winter clothes and decent boots.
There is also a stretch of rather stylish 1880s-90s working-class apartment buildings in the Grünerløkka area (and more upmarket ones in the Frogner area on the west end of town), and a very picturesque area of small-town wooden houses in nearby Rodeløkka if these are of any interest.
