Helsinki for 2-3 days in May or June

For what you are seeking, I'd much prefer Stockholm or Bergen to Helsinki (to stick to Nordic cities). Copenhagen should be good for this too, but I haven't been in many years, so it's hard to compare. If you do go to Helsinki, you should enjoy the food market area near the port (my favorite thing, much more than the various "sights," many of which were only OK).

To see the Northern lights, you need to go in the autumn or winter. And a bith further north in the Nordics than the capitals. Abisko is in my opinion the best place to see them.

In June it doesn't really get dark so no northern lights. On June 1, sunrise is at 4 am and sunset at 10.30 pm. In between you have twilight, but not darkness.

Harold's right. Those cities are much more likely to please you. Take into account that even in June, the evenings are likely to be chilly in all those places. I was in Stockholm around June 20 and the restaurants with outdoor seating had heaters and blankets for patrons, and we were very happy they did.

I would not go over the weekend of June 21. At least in Helsinki, most of the city goes out into the country to enjoy and celebrate the mid-summer holiday. Even though the market was fairly active in the morning, the city felt empty and about half the sights were closed. So the people you'd be watching would be mostly tourists who hadn't planned well. Or - like me - on a cruise port stop (you win some, you lose some).

You have a long list of what you don't care about and a very short list of what you do like to do. I found Helsinki a comfortable place to walk about and enjoyed sitting at an outdoor table having my second pear cider watching the Finns enjoy a sunny Easter weekend. However Finns who want to enjoy Finnish food just eat at home.

For people watching, Finnish families seem to enjoy the open air venues as much as tourist. The ferry ride to the Suomenlinna island world heritage site and walking about is a gentle way to spend an afteroon.

https://www.suomenlinna.fi/en/

Another open air venue that the Finnish families seemed to enjoy is the Seurasaari Open-Air Musem on an island at the outskirts of city center.
https://www.kansallismuseo.fi/en/seurasaarenulkomuseo/frontpage

I love Helsinki, but mostly for the astonishing quantities of outstanding Jugendstil/Art Nouveau architecture. If architecture and design of cityscapes aren’t your bag, there are nice cafes but Stockholm seemed more focused on cafes and people watching.

Thank you all for your great advice. It seems like Finland is not for us. We have been to Copenhagen and my wife has been to Stockholm and Oslo also... the search continues.