Bergen is Norway's "second city" and relatively unknown to those that haven't traveled to Norway. In my opinion, it's even more stunning than Oslo, and makes for a great weekend destination in the summer.
Here is a recommended itinerary if you only have a few days. If you have longer, I would recommend day trips cruising and hiking the fjords. You can also take the scenic Flåm Railway inland, either on a day trip or all the way to Oslo.
Arrive at the airport in Bergen and take the public bus to the city center.
Bergen is small, so wherever you stay should be walking distance from everything. If you would like the option to take buses you can get the Bergen Card which gives you access to public transport and entry to some sights. There are a number of hotels near the waterfront, or get an Airbnb in the Stølen neighborhood for a quieter stay.
When you are settled, head to the Bryggens Museum--Bergen City Museum. This is the starting point for guided tours of the original part of the city. You'll see some museum exhibits and learn about the city of this important port city as a powerful member of the Hanseatic League of trade ports in the 1300s. Then you'll go outside to explore some of the orignal and reconstructed buildings.
After your tour, imagine that you are one of the cod fisherman you just learned about, as you explore the picturesque waterfront and wander the outdoor seafood market. Grab some of the freshest and cheapest seafood available in Norway as you eat at the tables in the market.
Get up early to beat the lines of tourists taking the funicular up Mount Fløyen. It's only a 6 minute ride, but it beats walking uphill! Enjoy the spectacular views of the city and the fjords before taking a hike on the nearby trails. There are some great playgrounds for families up here, too!
After your hike head for lunch of Norwegian heart-shaped waffles with fruit and many other toppings at Waffle House.
In the afternoon, do some souvenir shopping in the Bryggen neighborhood, or general shopping on the Torgallmenningen pedestrian mall.
In the evening it's time to get out on the water! You can combine a seafood dinner with a half-hour boat cruise to the Cornelius Seafood Restaurant out of town in a tranquil setting. Alternatively, have an early dinner in Bergen and take a three-hour evening fjord cruise. In summer the sun sets very late here, so you’ll have plenty of time to enjoy your cruise on the water and the beauty of Bergen’s natural setting.
Stretch your legs with a stroll through the city along the Festplassen park and hopefully catch some live music. Climb the stairs to St. John's church for some views and from there you can walk through the University of Bergen.
If you have time before your flight, enjoy lunch or a coffee as you sit outside and people watch in Bryggen.