First of all, how nice that you are planning to visit Sweden and Denmark!
As for Swedish zoos, I can write about the most known zoos here and their star attractions if that's any help for you:
Kolmården Zoo & Tropicarium
The biggest and most extensive collection of species in Sweden. The park is located outside the city of Norrköping, and it is possible to arrive here by train and bus. Trip from Stockholm, the capital, takes about 2 hours.
Famous animals here are the Gorillas, the Snow leopards, the Safari ride (cable car where you can see lions, giraffes, zebras, ibex, moose, bears and wolf) and the Dolphinarium, home to a group of Bottlenose Dolphins. Don't miss the seal pool, housing three species in a very deep pool. Other animals that you can see are tapirs, red pandas, rhinos, chimpanzee, camels, meerkats, tigers and takins among others. Whether you like it or not, this park is also home to the biggest wooden roller-coaster in the world; Wildfire.
After visiting the zoo, don't forget to see the Tropicarium next door. Here you can see a very impressive collection of snakes, alligators, lizards, turtles, fish, sharks, birds and smaller monkeys.
Kolmården is a must see for you if you are coming to Sweden!
Parken Zoo Eskilstuna
Another famous zoo, close to Stockholm, is the Parken Zoo in the city of Eskilstuna. This zoo is most famous for showcasing many rare species to the Swedish zoo visitors (they did have giant pandas once). They have the only Giant otters, jaguars, clouded leopards, drills, sand cats, fishing cats and Visayan warty pigs in Sweden and is well worth a visit! New this year is a enlarged children's zoo, including goats, pig, alpacas and also camels as a new species. The walkthrough for lemurs is very good too!
Borås Djurpark
My clear favourite of Swedish zoos, Borås Djurpark is also a must see. They are specializing in African fauna and has a very good collection of that. Their savannah featuring African elephants, giraffe, zebras, antelope and also buffalo is stunning. Also their mixed enclosure for White rhinos and cheetahs is a must. Lions, hyenas and African wild dogs complete the African carnivore lineup, and you can't miss the Scandinavian wilderness with brown bears, wolves, lynx, wolverine and moose when you are here!
The monkey house keeps small groups of Chimpanzees, orangutans, Sulawesi Crested macaques and white-handed gibbons. Other species include bongo, red panda, Amur tiger, European bison, penguins and a children's zoo!
To come here, take a bus or train from Gothenburg Central Station, will take you about one hour!
Nordens Ark
I haven't visited this zoo in many years, but if you are in the area, I recommend you to visit! My fondest memories from last time visiting here are the Snow leopards, the Amur leopards, the maned wolves and the Wetlands house. They also keep Amur tigers now, which is a must see!
Skansen/Skansen Aquarium
The zoo/open-air museum of the capital Stockholm is also a must see for you. You can see the Swedish fauna like bears, wolf, lynx, wolverine, moose, European bison, otter, owls and more, while also visiting old Swedish houses to learn about our history.
The Aquarium is inside the park, it does have a separate admission, but is very worth visiting. During the years, many rarities has been calling the building their home (koalas, echidnas, tarsiers, slow loris etc). The highlights nowadays have to be the Sacred baboons, meerkats, ring-tailed lemurs, dwarf mongoose, feathertail gliders, sloths and the small monkey species (bolivian titi monkey, golden lion tamarin, pygmy marmoset, cotton-top tamarin and white-faced saki). Also outside the aquarium, easily missed, is the enclosure for a small group of Colobus monkeys.
There are also some smaller parks, which you might want to visit, it's all up to you and what you want to see.
Furuvik
While not the biggest zoo in the country, Furuvik is a nice little park outside of the city Gävle, 1 hour and 30 minutes from Stockholm. The big highlights are the enclosures for Chimpanzee and Sumatran orangutans (which recently had a baby, the first one ever in Scandinavia for that species). The small rainforest house is ok, not a huge collection, but quite good for a smaller zoo. Camels, grey kangaroos, barbary sheep, alpacas and saki monkeys are also animals you can find here.
Universeum
It's not really a zoo, more like a museum/science centre with animals. If you are visiting Gothenburg, you might want to visit this place. They have a large indoor rainforest featuring tamarins, sloths, many toucan species, ibises, caimans, anaconda and many other species. The large ocean tank featuring sharks is also nice, and also the Way of the Water exhibition is nice, showcasing the Swedish nature and also some smaller reptile and bird species can be found here.
/ Swedish Zoo Fan