In October/2018, I was on Westerdam cruising from Alaska to Yakohama, and our ship called on Hakodate for a day.
It is true that which wharf the ship docks depends on what other berths have been taken. In 2018 we docked at the Ichiei (一映) wharf, 2.8 km north of the city center, but the port authority provided free shuttles to the JR Hakodate station. One way ride on the shuttle took 20 minutes. However, your ship may be able to dock within walking distance of the morning market, which is next to the JR Hakodate station.
I visited the morning market first, therefore I did not see if any local operator was looking for business in front of the JR Hakodate station. By the way, there is a TI office inside the JR Hakodate station.
To get around Hakodate, you may take a tram or taxi. Taxis won't be expensive because the distances are short.
To get to Mt. Hakodate, you may take a tram to Jujigai then walk to the ropeway station, or take a taxi directly to the ropeway station. Buses will be sparse until after 4 pm. But, google the ropeway's schedule first to see if it is operating on the day when you are in town.
From Google Maps, the closest tram stop to the City Museum of Northern People is Suehirocho, just one stop after Jujigai on tram # 5.
If you prefer a guide, contact the Hakodate Goodwill Guide Association to request a guide ahead of time. They offer a 4-hour "Good Will Guide" tour for 5000 yen per group, and you'll pay the guide's food, entrance fees, transportation fees etc.
https://hakodategoodwill.wixsite.com/hakodatesgg
