I had some of the best sashimi and hotate in the fish market here. This touristy seaside town is pleasant to walk through. There's a brewery, which unfortunately was closed when we arrived, though I was still able to try some of their beer from a market. Hooray, no public drinking laws! One of the main attractions is heading up the cable car to the top of the mountain for a view. We didn't do this, but I imagine it's quite lovely up there.
Hakodate Have historical site Goryokaka Park and can view Mt. Hakodate, it is fantastic and famous night view.
Hakodate has a small town feel compared to big cities like Tokyo, yet has some notable sights to see. It has a great public transit system utilizing buses and streetcars with maps at each station that highlight city monuments and popular things to do. Stop to eat breakfast at the morning market. Try a seafood donburi! You will surely be back every morning. Visit the Kanemori Red Brick Warehouse for souvenir shopping and pier views. Eat a burger at Lucky Pierrot and have a drink at Hakodate Beer Factory. Be sure to order their grilled squid to share.