Norway Fjords

I was on a cruise liner - Norwegian fjords/Shetlands/Iceland from June 21. Weather's always variable. I had pleasantly warm, sunny days throughout. Norway is about the most expensive country in Europe - even for snacks and drinks. If it helps, our stops in Norway were Bergen (a not-so-small town with interesting sights and the Munch museum), Flam (beautiful sail into the village through the fjords, very scenic train up into the mountains and back), and Geiranger (another beautiful sail through the fjords, then a bus up through the mountains and snow fields - very cold). I haven't been to Oslo. On a different cruise I enjoyed a day in Copenhagen and loved Stockholm

We spent a little over 3 weeks in Norway this summer on a home exchange and yes, it is quite expensive. If your rent an apartment and cook for yourself then that will cut your costs considerably. Food at the grocery store is comparable to what I pay here in southern CA. Eating in restaurants is a whole different story...we never got out of a meal for our family of three for less than about $60-70.
For the amount of time you want to spend I would allot 3 days (4 nights) to Oslo - it's one of my favorite cities in Europe...very warm, inviting and low-key with plenty to see and do.
Take the train from Oslo to Bergen...amazing trip!
Bergen really doesn't warrant more than 1 day (2 nights) IMHO - after you've seen the old Brygge buildings along the wharf with all of their touristy shops, walked around town, and taken a ride up the funicular, there isn't a lot left to do in town. There are a couple of historic homes to see outside just of town, most notably, Edvard Grieg's house. If you like to hike then there are many trails from the top of the funicular with some pretty spectacular views at the top!
Most of our time this summer - about 3 weeks - was spent in Alesund. What a spectacular area! The town itself is small - you can spend one full day exploring. The town is easily walkable and is Art Deco in style...the whole place burned down in the early 1900s and was rebuilt. Nice shops, antiquing, restaurants, and a great view from the top of the funicular. There is a beautiful little outdoor folk museum just outside of town on the fjord with old buildings from that part of Norway that have been brought in and reconstructed, as well as Viking ships that have been dug out of the ground locally.
The Alesund area has a lot to offer. There are many fjords nearby including the Geirangerfjord - spectacular! The drive from the town of Geiranger over the Trollstigen Pass road is not to be missed with it's spectacular cataracts, waterfalls, and the pass itself that has a modernist designed lookout and visitor complex that is, by itself, worth seeing.
Runde Island is one of the largest bird sanctuaries in Europe - windswept and beautiful. You can hike all over it or take a boat around to see the birds and cliffs.
There are many other small islands to see in the area, most of which are connected to the mainland by bridges or tunnels. There are farms, small churches (don't expect them to be open that early in the year), beautiful boathouses on the water, lighthouses - lots of opportunity for photography if you like to take pictures.
Where there aren't bridges or tunnels, an excellent car ferry system connects the whole area so that you don't spend too much time driving around the huge bodies of water that are everywhere. Most of the ferries are used by the locals so they run year-round - a few, like the Geirangerfjord ferry, are seasonal, tourist ferries, so you would want to check to see if they are running in late May-early June.
Besides those things, the hiking and skiing in that area is also very good. You might just catch the tail-end of the ski season. The Norweigians hike even in the snow...they take their skis and just head out all over the place, taking along little cookers and making pancakes in the woods. The certainly know how to embrace their environment!
Now that I've said all of that my only worry is that you are traveling early in the season so you will run into snow and rain - even in summer there are just as many rainy days as sunny days! It won't be warm.

We found cruise ships to be the best way to see the region. Food in restaurants is deadly expensive. We went to TGI Fridays and had a burger and coke--$30 each. Cokes are $4--about the same as beer. In a restaurant, a beer's $8. I now know why there are no fat Scandinavians--they cannot afford to eat.

We took the Norway in a Nutshell trip. We took a 4 1/2 hr. train ride, and the scenery was very beautiful. Then we took a train from Mydahl down to Flan--the highlight of the trip with incredible scenery. Our 4-5 hr. fast ferry ride was through pretty scenery, but the fjords were not the most beautiful mountains I've ever seen. I'd been just as happy to have ridden the train back up the mountain and caught another train straight into Bergen.

We really liked all the cities visited--no losers here. St. Petersburg is an incredibly beautiful town. Fortunately, we had 18 days of fabulous weather in a month where 2 out of 3 days usually see rain.

I would suggest that you would be better off in the southern parts of Norway at that time. Worth considering; travel a few days earlier to take in 17 May - the national day (constitution day) - the national costumes are on show in the processions. It is particularly based on the schools and other young people activities. Oslo is probably best location for you and a good starting point to see the best of Southern Norway. There are now 2 new World Heritage sites, based on the initiation of the second industrial revolution, in Rjukan and Notodden in Telemark. Rjukan was also the site of the Heavy Water production (essential for the Germany's effort to make an Atomic Bomb in W.W.II) and the sabotage efforts.
Although car-hire is, as everything in Norway, rather expensive, it would probably be cheaper and more effective than relying on limited access afforded by public transport - plus hiring a cabin would maximise your exploration opportunities and also keep the overall costs more manageable - particularly as you will be here before the school holidays. Bye the way, the recent fall in the exchange rate for NOK helps a lot. Norway is in general a 'child-friendly' country with special emphasis on children activities like special exhibits in most museum.
I would also suggest that you look up 'Visit Norway' and the various regional branches (eg 'Visit Telemark'). They should also be helpful in providing details of accommodation and specific information relevant to your interests and family make-up.
Enjoy your exploration and marvel at the nature. One thing to be aware of - Norway has an awful lot of wild nature and most is not 'sanitized'!

We went to Norway this year at the end of May very similar to your timeframe. We stayed in a cabin fjord side in Aurland. While the cabin was slightly more expensive than a hotel room, we were able to make dinner right in our cabin. Aurland is near Flam. This was a great home base for hiking, fjord cruises, and exploring the area. The weather was not optimal. But with rainproof and warm clothes, we had a wonderful time. I can't stress the importance of proper clothing. We were told that it was a bit colder than usual this year.

To help with your costs you might look into the possibility of having a home base and explore from there with a few overnight trips. There are a lot of people from Norway who are on home exchange agencies. We get contacted by a few families every year with some very desirable locations and homes. Many like to come to sunny, warm California.

Thanks for all the help and suggestions. I love to travel so much that any possibility to take a trip I jump on, and hard! But, with more review, I think we will have to wait until we can save more money. We just are not quite there yet even with the good airfare. I'll save all the good ideas until then.

Thanks again!