We have 3 1/2 days to go to one European city before going to Gothenburg, where should we go?

London and Copenhagen would both be very good choices. Stockholm and Amsterdam would work well too. Oslo as well.

Been to all of the above. We much better prefer Colenhagen.

It might be helpful to know "why Gothenburg," or how you are arriving in Europe. (Please put your home in your profile so we can see it.) But I'd suggest you focus on affordable, low-effort transportation - either rail or discount air, whichever you usually prefer. (Discount air choice is affected, for me, by my expected luggage size.) For example, when planning our last trip, I was surprised to see how well-connected Copenhagen was to Düsseldorf. I didn't even worry that much when Air Berlin announced their (future) bankruptcy plans, because other airlines also covered the jump. There are many pleasant "secondary" cities, like Düsseldorf, that combined with their day-trip neighbors, are more than good enough for 3 1/2 days. It takes research to learn that.

I am hopelessly biased.....I love Oslo!
Easily reached by train or bus.

Maybe Prague, BoBo. Are you really BoBo?

So much depends on what you like. I can never get enough of London or Paris. I wasn't very impressed by Copenhagen, liked Stockholm much more. In early April you might get lucky with the tulips in Amsterdam - good city for 3.5 days with day trip options if you get bored. What about Berlin?

As Tim said, transportation is important, and as everyone is saying, you should go where YOU want to go for 3 1/2 days. We can all throw darts, but we need more information to give a more focused response.

Stockholm, Copenhagen, and Oslo are obvious choices, as they all have good train links to Gothenburg, as well as several days of sights. With a flight, however, you can go lots of places. And by early April, the weather will be good (or good enough) in many places. So, what calls to you?

If you want ideas, here's the list of nonstop flights to Gothenburg's airport: https://en.wikipedia.org/wiki/G%C3%B6teborg_Landvetter_Airport#Airlines_and_destinations

I usually think along the same lines as Chani, but not on this. Copenhagen is my favorite city in Scandinavia. There is more to see and do in and around Copenhagen than any other Scandinavian city. I liked Stockholm and Oslo, they're both somewhat more scenic, but I felt I wouldn't want to spend much time in either. I can see her opinion if you stay near the train station, which is fairly seedy. Plus Tivoli was disappointing. Stay near Nyhavn and use the metro to get back and forth to the airport.

Early April will likely be dark and wet - which points me toward somewhere with more indoor activities. The national museum, glyptotek, Rosenborg, Amalienborg and nearby Frederickborg and Kronborg castles and/or Roskilde Cathedral and Viking ship museum should provide plenty to fill your days. The Copenhagen card covers admissions and transportation to all of those and more.