Towns in between time in Stockholm and Copenhagen

Family of four with two teenagers planning August trip to Denmark and Sweden, flying into Stockholm and out of Copenhagen. First time for all of us. I'm planning five nights in Stockholm and five nights in Copenhagen, which leaves us three nights in between, traveling by train. We'd like to have an interesting spot or two in a charming, smaller town or beautiful, small city where we can relax but also see interesting sites (art/history) either nearby or easily accessibly by train. Our daughter likes beaches, the three of us are less interested, so a beach location with things to do other than the beach could work. We are not planning on having a car for this trip. To give some context for the types of smaller towns/experiences we enjoy: Northeast Harbor, Maine (on the quiet side of Mount Desert Island/Acadia - not Bar Harbor); Charlbury, England (edge of the Cotswolds, rail access to Oxford); Concord, Massachusetts (walkable, quaint, history); Williamstown, Massachusetts (art). All that said, a friend of mine grew up in Gothenburg and recommends it highly, so while it's another city, I haven't ruled it out or other cities. Also am open to overshooting Copenhagen to visit cities/towns in Denmark. Some places I've read about are Ystad, Lund, Almhult (IKEA museum for my kids), Aarhus, Uppsala, but the more I read, the more possibilities open up! Thanks in advance for any ideas this group has.