Ulriken and Fløyen are two of seven mountains around Bergen. Aaaand, of course -- it turns out that Norwegians are crazy enough that there's an annual event to hike all seven peaks in a single day, for a total ascent of 2,400 meters over about 26km.
We learned this first hand, because it was completely by coincidence that we did the Vidden hike on the same day as the 7-mountain event. Here's the route they take, and the rather less strenous route we took, below.
The Vidden trail is an approximately 15km alpine hike that runs around part of Bergen from Mt. Ulriken to Mt. Fløyen (or vice-versa). With a cable car at the Ulriken side and a funicular at the Fløyen side, you can spend the entire hike at altitude, saving your knees from much of the ascent and descent (although not entirely all of it).
We walked it in the direction from Ulriken to Fløyen, which I highly recommend, because it means you're ending the hike in the center of Bergen, where you can easily pop into a cafe, restaurant, or wine bar to recover.
We never found a good map of the trail, but it's very easy to follow at a macro level - there are huge stone cairns marking the way, and I do mean huge -- usually two meters tall and at least meter across. They have to be big enough to poke up through the snow in the winter! So knowing which direction to go is never a problem, but sometimes finding the precise trail is - it's popular enough that it's quite heavily braided at times.