You can get a dramatic view of Hakodate and surrounds from the summit of Mount Hakodate, which rises up on the city's southwest side. The "ropeway" aerial tram takes you about a half-mile up for great panoramic views. The site is particularly popular at night, so you may have a wait after sunset.
If you're in Hakodate for cherry blossom season, head to Goryokaku Pentagonal Fort and the surrounding park, which is filled with cherry trees. You can get a bird's-eye view of the fort and blooms from atop neighboring Goryokaku Tower.