Bergen to Alesund or Trondheim?

Trondheim is worth a stop. But I'd suggest the train from Trondheim to Lofoten instead of flying.

In case you are not aware, there are overnight ferries from Bergen to Alesund. The trip takes roughly 12 hours, departing around 8 PM. If you choose to do so, you can remain on the ferry (I assume at additional cost) while it spends the day diverting into the Geirnagerfjord and stops a second time at Alesund. The ferry cabins are tiny but comfortable enough--though I'm quite short and don't know what the bed would be like for someone tall. My Hurtigruten ship had a great lounge with huge windows giving a great view of the trip through the Geirangerfjord.

I'm nuts for Art Nouveau architecture, which is Alesund's claim to fame. I very much enjoyed my day there.
If that sort of architecture doesn't particularly appeal to you, the larger city of Trondheim might be a better choice. Trondheim's an overnight ferry ride from Alesund, but that's not the most efficient way to get there if you don't want to see Alesund and/or take the Geirangerfjord detour.

I have nothing to contribute with respect to the logistics of traveling to or from the Lofotens. That seems like a very attractive area, but I felt it was a bridge too far for me last year.

Last year I rented a car in Bergen and drove around some fjords, ending in Alesund. There are many route options depending on what you want to see, what you want to do, and how much you want to drive. I dtove to Flam via Hardangerfjord on the first day, making a couple short sightseeing stops. Stayed in Flam 2 nights and did a fjord cruise and Flamsbana. Then drove up Stegastein, over the snow road, stopped to see a couple stave churches and ended near Loen. Did the Skylift the next day, Dalsnibba viewpoint, the ended in Geiranger. Then drove Trollstigen to Molde, next day drove to Atlantic Road, took some smaller local roads and then arrived Alesund. I had 9 Days that started with a stay in Bergen. My longest driving day was closer to 5 hours (on the road, not counting stops) but I was able to schedule others for 4 hours or less. I never was tired and scenery was fantastic the whole time. You could also look at the cruise/ferry options but I liked being able to decide places I wanted to see and how long I wanted to stay. I also like the ability to change route on the fly if I felt I had the time to add something or preferred to nix something and get to next destination sooner. I’ve heard some people take the cruise to Alesund and then rent a car there to do a loop to Geirangerfjord and back. Again, I wanted to see more and have the option to linger some places. I have fantastic photos mostly from the little side trips I made along the way. Norway is beautiful and you’ll have a great time.