I live in Oslo.
It is expensive but if you want to do it on the cheap its possible. Avoid eating and drinking out. Difficult to get accommodation in the summer, book early and shop around. Otherwise prices are similar to Dublin prices.
If your here for just a weekend, you will most likely only get to see Oslo. Or at best take in the Norway in a nutshell tour (round trip bus, train, boat trip from Oslo to Bergan) that takes in a lot of the postcard scenery.
If your here longer there are plenty of sights to see, only problem is everywhere requires a lot of driving to get to.
On the west coast you can see
Prekistolen (located near stavanger) 2 hour hike to the top..
http://www.preikestolen.no/
Bergen - Nice town on west coast.
http://www.visitbergen.com/default.asp?sp=NO
Trollsteigen, road that winds down mountain
Gerianger fjord (located between bergen and trondheim) .. post card fjord
Lofoten (near Bodø) --
East
Oslo - Frogner park, nobel peace prize museum, ski jump, frognerseteren, arker brygre, new opera house (only open a few months), munch museum.
www.visitoslo.no,
www.norway.com.
South
The south is nice too, its more sea side towns though, not the kind of thing norway is known for..
These are the big ones, Its alot of driving with a lot of mountains in the way..
Ryanair fly into Torp an airport 1.40 mins by bus south from Oslo. Usually the cheapest tickets but the times of the flights and the time it takes to get to the airport means you loose a day traveling. SAS fly to an airport 20 mins (by fast train) from Oslo. Faster but more expensive.
kk