Must do's for a day in Tromso, Olden & Trondheim

I have not yet been but hoping to do a cruise eventually.

Have you searched the forum?. Go to the top where there i a search bar and just type in Norway. You are going to get a lot of results. And then you can narrow them down.

I also suggest youtube videos. They are so helpful and informative.

Many members on forum have written about Norway and I expect they wiill jump in with tips and advice.

Nidaros Cathedral in Trondheim.

At Tromso you dock at Breivika which is about 3 miles out of town. This is unlike Hurtigruten/Havila who dock in the City Centre.
The ship will doubtless run a shuttle bus at a steep charge, but there is a public bus line, #42. Buy a city day pass on that first bus. It currently costs 133Kr.
If purchased on the bus as far as I know it still has to be paid for in cash. But it can also be bought in the app.
The bus company is called Svipper.
I suggest going to the Cable Car (the Fjellheisen) if it's a good day using bus #26, a circular route.
There is also the Botanic Gardens - I walked there in mid winter when everyone, locals included, was sliding and falling everywhere but there are buses.
Yes the Arctic Cathedral is on most people's itinerary, but don't forget the Domkirke in the City Centre. I've not been there as a tourist, but for Christmas Eve service with the entire ships company from a Hurtigruten ship- crew and pax. The Domkirke is apparently the only wooden Cathedral in Norway.
Six bus routes run over the bridge to the Arctic Cathedral, so service is very frequent, or walk across the bridge as I did.
Historically Tromso was a whaling and expedition centre. So to me the polar museum (in the old Customs House) should be high on your agenda, as should Polaria. No I have run out of time to get to Polaria.

In Trondheim apart from the Cathedral I suggest Kristiansen fortress and also Munkholmen Island (by ferry).
But also the Grakellbanen tramway (part of the City transit) up into the hills with great views.
I would do that first and walk the 4 or 5 miles back into the City on the last part of one of the very long pilgrim trails which led to the Nidaros Cathedral - the burial place of St Olav, the patron saint of Norway, thus a key Pilgrimage site.
I also recommend the Folk Museum- Sverresborg Trondelag.