15 sleeps in Norway & Denmark - best itinerary/route/transportation suggestions???

Sounds like you already have time allocated for "city sights". You want "quaint areas and gorgeous views" in addition? Since you've done NIN you know that Norway's fjord country is full of those. I'd suggest a jaunt from Bergen either up or down the coastline to whichever new fjord area interests you the most. Some have been designated as UNESCO World Heritage sites which may be a hint. Norway has also helpfully designated 18 of what they think are the most scenic roads in the country. See www.nasjonaleturistveger.no/en/. We picked a half dozen of those and used them to make a loop around the countryside we wanted to see. In July, we went from warm sea level to 4,000 ft elevation snowfields and ice covered lakes, multiple times. We saw small towns, mountains, quaint ferries, amazing tunnels (with roundabouts in them!), farms, sheep sleeping in the roads, huge orchards shimmering with plastic covers, freshly harvested strawberries for sale at roadside stands (no cash please, only credit cards), at least a dozen stave churches, villages with their own ski jumps and lots of scenic beauty. For my money, if you drive in and around fjord & mountain country, you can't go wrong. National Parks are also good areas to consider. I'd look at online Norway resources and other guidebooks beyond RS for more info about out of the way areas. Multiple posters have made specific recommendations about favorite countryside areas on this forum. Have a great trip.

Thanks on this! I take it you drove for your entire trip? And I actually haven't done NIN -- just saw advertisements for tours which were really expensive, so plan to do it on our own. This is our first trip to Norway so looking for a route around the country once we leave Oslo. And the best way to do NIN...

May I ask?
- Where did you fly into?
- Can you tell me what your stops were along the way between cities?
- Any lodging recommendations?

Thank you again.

Now that I reread your first post more carefully I see that you said that you are "aware" of NIN, not that you've "done" it. My mistake. But onward: Everyone and their own situation is unique, so I'd suggest that you read over all the Trip Reports posted in the last couple of years that were in Norway or Denmark. You can find my complete report under "Scandinavia 23 days", but other posts are just as worthy of reading if not more so because I tend not to discuss "everyday" stuff that is well covered by others. In my Reports I like to talk about things that surprised me or topics that other posters don't mention. There have been a large number of posts under Norway about NIN in particular, so look at those. We did our own (longer) version of NIN so I have no comments about the "official" tour.

Since you asked I will provide a very quick summary of our trip, but please do check other posts and other info resources. We flew into Copenhagen, spent 5 days there on foot, took a train to Stockholm for another 5 days on foot, train to Olso, 5 days on foot, then rented a car for a trip out to Bergen followed by a big loop 7 days through mountains & fjords back to Olso for flight home. You of course have less time, but you've dropped Sweden so your time in Denmark & Norway is comparable to ours. We were looking for a combo of city and country, but ended up front loading all of our city time mostly without forethought. For a do-over, I'd separate time in Olso & Bergen by putting them on each end of the loop, instead of both in front. Between Oslo-Bergen-Oslo we stayed typically in small towns - big enough to have some options. Of course, that's about all the habitation there is out in the country - besides the villages and farms. I don't have a lot of lodging recommendations, except to say that the Thon hotel chain in Norway has gotten some good press in the Forum, we stayed at one in Oslo and one near Lillehammer and were quite pleased. Also if you read my complete report, you will see that I raved about the deal we got by staying in a ski town in July - a fantastic suite for a great price.
If you'd like more info beyond what is in my posts, feel free to send me a PM and I will be more detailed than I am here, e.g. I will yak at some length about the National Tourist Routes if you let me.

This sounds similar to my itinerary this summer...Denmark and Norway for two weeks...but we're not rending a car, just public transportation. We're starting off in Copenhagen and then ending our trip in Bergen. (We decided to do 4 days in Copenhagen and only 2 days in Oslo because there were more things in Copenhagen that we wanted to do.)

Start off in Copenhagen (enjoy the city, but maybe take a daytrip somewhere, perhaps to Roskilde, if you're interested in seeing their Viking Ship museum or Helsinore looks nice too)

Overnight ferry from Copenhagen to Oslo will save you some daytime (leaves Cop at about 4:30 in the afternoon and arrives in the morning in Oslo). I've researched the ferry and it looks pretty nice.

Oslo -- folks museum, Viking ship museum, Vigeland Park with sculptures and a museum

Oslo to Bergen via "Norway in a Nutshell" (you could stay overnight somewhere, perhaps Flam, if you want to do this slowly and not do NIN all in one day). We're taking NIN slow and doing it ourselves and there's lots of threads on this forum with good advice about NIN. I've learned a lot from others on here. We decided to stay in Flam, but if you're staying in Flam then I would recommend that you try to book a room soon because we had difficulty finding a "cheaper" option for July. We're actually going to stay at the hostel there. We chose Flam for 2 reasons...it is along the NIN route and it looks beautiful. I hear there are some nice trails in and around this little town too and we like to do moderate hiking trails. You can book all the trains, boat, and bus yourself. For NIN, it's 2 trains to Flam (Oslo to Myrdal then Myrdal to Flam). From Flam, you can take the scenic boat ride to Gudvangen, then the bus from Gudvangen to Voss and a train from Voss to Bergen. I believe the website for booking trains is nsb.no (we haven't booked yet) and I've heard that US credit cards have been a problem for some when booking train tickets online so you can call and book them over the phone too. I've also heard that the train from Oslo to Myrdal can sell out, so we're booking that one ahead and you can book it up to 3 months ahead. I'm sure all the trains are scenic, but the highly recommended train ride is from Myrdal to Flam. Visitflam.com has info about the boat option. The popular boat route is Flam to Gudvangen, along the Naerofjord and this fjord looks unique and beautiful because it is so narrow.
Have a fun trip!

I’m not quite sure what you meant by “joining a formal tour” on the NIN route. The NIN is just a coordinated transport to see the fjords. There is no tour guide. You can do it in one day or slow down and take several days, staying in one of the quaint towns like Flam, Baelstrand or Solvorn.

As noted above the NiN is not a "formal" tour with a guide or even a fixed itinerary. Even if you use a NiN booking service (e.g. Fjordtours) to coordinate you itinerary, you can do the NiN as a one way in either direction or round trip. You can do the NiN as a 24 hour round trip or as a multiple day tour with stops along the way.

https://www.norwaynutshell.com/original-norway-in-a-nutshell/

Hotels & accommodation

We highly recommend adding an overnight stay to your tour!

Prices & tour variants

Press «Plan & book this trip» to see the different variants of the
tour and the specific price for the tour you prefer. There is no guide
on our tours, nor group-, senior- or student discounts.

And if you know what you want and how to do it, there is the do it yourself booking option.

Back to your fundamental question. Starting point is buying a couple of Scandinavian guidebooks - Rick Steves, Lonely Planet etc. Identify your must see/do list and start planning. If you are an active traveler, Norway and Denmark have numerous outdoor activities from hiking Norwegian glaciers to bike touring Danish islands. For example:

https://www.norwaynutshell.com/sognefjord-in-a-nutshell/glacier-trip/

This summer you can take the Sognefjord in a Nutshell tour in
combination with an exciting guided glacier tour to Nigardsbreen! On
the tour you will also experience the entire length of the mighty
Sognefjord on a boat trip and enjoy spectacular views from Flåmsbana!

This trip is available from Oslo or Bergen. Starting from Bergen, you
will among other things experience a beautiful boat trip on the
Sognefjord and a spectacular train journey on the legendary Flåmsbana.

Glacier hiking on Nigardsbreen

From the Breheim Center you embark on your glacier hiking trip!
You will receive all necessary equipment and an experience guide will
give you an introduction to glacier hiking and safety on the glacier.
On the glacier you can experience and explore the finest glacier
formations and enjoy spectacular views! The glacier hike is suitable
for most people and is not particularly hard or demanding.

And I should add that unless you have an unusual teen, your teen should contribute to the must see and must do list and not just get dragged around from one museum to another.