Best stop overs after Best of Scandinavia tour?

There are many options and it's hard to give advice with such an open question. Especially since it depends a lot on what you are interested in.

Could you spend extra time before the tour? It is easy to get to Stockholm from both Tallinn and Helsinki by overnight ferry. You could start your trip in Helsinki, continue to Tallinn, and then take the overnight ferry to Stockholm prior to the start of the tour. The overnight ferry from either Helsinki or Tallinn to Stockholm is very efficient for travel and usually costs less than a hotel night.

If you are doing extra time after Bergen, then I’d see what cities are served by non-stop flights from Bergen. Looking at the airport wiki, it looks like you could possibly get to Riga, Krakow, and Helsinki on non-stop flights.
https://en.wikipedia.org/wiki/Bergen_Airport,_Flesland
I’d first see what the flight options are and go from there.

I can spare another 3-5 days after the tour ends and need to be near a decent airport to get home to the west coast.

It matters whether this means California or someplace else.

Since KLM flies from Alesund, Trondheim, and Bergen to AMS then nonstops from AMS to the West Coast any of the 3 main cities outside Oslo will work with one stop getting home. Similar with Lufthansa probably.

Wow- these are super helpful, especially the airline routing tips. I am not so familiar with those tools.

My spouse and i have many interests, but probably don't want to duplicate our experience from the Scandinavia tour-not to paint a broad brush, but in Italy you can get too many churches over the course of a tour, and castles in UK, and the like. I tend to like textiles and the decorative arts, and usually search for fabric stores in countries i visit. I also love hiking and the outdoors but hard to do a city tour and then also cram in a hike. Diversity of culture is interesting to me, and also seeking out newer and less crowded or discovered places. We loved Romania for this reason.

Last question, likely most appropriate for Badger, but I have some friends who live in Gothenburg, but the Rick Steves tour passes through Varburg only for one evening, and it looks like its a very narrow window so diffcult to coordinate. How easy is it to get to Gothenburg from Stockholm if we arrive there and try to meet our friends for a half day?

How easy is it to get to Gothenburg from Stockholm if we arrive there
and try to meet our friends for a half day?

Very easy, 3 hours by train.

We're scheduled on this tour in July. Because it's difficult to get to our East Coast airport from anywhere, we decided a several days layover in Paris was the easiest option.
We're flying into Helsinki for a few days prior to the tour starting, then taking a quick flight into Stockholm. The Bergen airport has limited options for our time frame which is why we opted for Paris at the end.

then taking a quick flight into Stockholm.

You really should take the overnight ferry to Stockholm. The archipelago views alone are worth it.

We took the morning train to Oslo, beautiful trip and the over night ferry to Copenhagen. We started our trip in Copenhagen and then took the train to Stockholm to begin the RS tour. We really enjoyed the extra time in Copenhagen and Oslo.