2 weeks in Norway and Denmark
 

I just booked a flight to Europe in April 2020 and I am interested in visiting mostly Norway and Denmark. I have 2 weeks total and as I don't drive, I will be limited to tours and public transportation. Right now, I'm thinking about seeing Oslo, Bergen, Stavanger and Copenhagen. How should I split my time? I mostly just want to experience the local life, enjoy the big cities and see some natural wonders.

Thanks!

I haven't been to Norway yet, but for Copenhagen, you might start with a first rough estimate of 3 or 4 nights for the city itself (depending on your interests) and another day or two for day trips (e.g., to Roskilde).

Enjoy!

With these four cities, seems like you are planning to spend most of your trip in Norway. So regarding this, I would suggest you add an extra city Alesund. I recommend starting from this absolutely beautiful city and you would need about 3 days here. I was able to explore the city itself in one day, I spent another heading to the Geirangerfjord and a smaller trip to the hjorunfjord and for the final day, I would think a quick detour to Jotunheim or josteldasbreen. This was one place I wish I went to during my trip.
Next head to Bergen, it's quite small, bit you would still need like 2 to 3 days for this city, you could use the first day to visit bryggen, thoroughly explore bryggen, the wharfs, the mount floyen funicular, the stave and leprosy museum are must sees as well. The remaining day or two, try some boating excursions. They are absolutely cool.
After bergen, stavanger isn't so far, a few hours by train. The street art of this city is truly remarkable and a full day should be dedicated to just soaking in the sights and houses. Another day can be used to check out the lysefjord alongside it's pupilt rock, so roughly two days as well.
Last in Norway, would be Oslo, here I recommend at least 3 days, there is just so much to see, from the bygdoy museum island to the oslofjord islands, the whole city itself is just beautiful. But I am sure you already know this.
Finally done with norway, here comes Copenhagen. I suggest nothing less than the 3 days too, I didn't want to miss a single important sight in this city (I am easily carried off track, and detoured) so I got lucky and stumbled on this tour website www.anastasia.travel, it's for this agency Anastasia tours and I have to say for my easily distracted self, it was one of the best decisions I could have ever made. I then used another day to do some personal exploring and get distracted or side tracked to my heart's content, not like I hadn't already seen everything I wanted to see but just soak in the streets et all. It was really really fun.
One thing I forgot to mention is that Norway can be quite expensive so please keep that in mind. Also, this is strictly based on my experience plus an added opinion so it's not compulsing in any way and I assumed the two weeks is minus the actual travelling down to Norway.
Hope you enjoy your trip and find this helpful.
Have fun

Where does you flight to Europe arrive? And where does it depart? 2 weeks total - is that 14 days (13 nights)? Does that including flying days? Do you have an overnight flight to Europe?
Without knowing that it is hard to give any advice really.

I fly into London where I will stay 1-2 nights and I fly back home from Dublin where I will spend 1-2 nights as well. I have up to 15 nights I can spend in Norway and Denmark.