There is a good hotel near the Shinkansen station called Grantia Hotel Ekimae in Hakodate. It's a 2-minute walk from the train station. It's reasonably priced and includes buffet breakfast. Japanese-style dinners are offered at Hana Tei restaurant. It features a public hot-spring bath with 13th-floor views. All have a bathtub, fridge and humidifier. Japanese-style sleepwear and slippers are provided for all guests. Limited internet access are provided free at the lobby. Since you will be staying for the night, don't miss the morning fish market. You can just stroll down the market lanes and browse through. Check the hairy crabs and other seafood that are on display including the famous red cuttlefish that some people eat live! Some vendors offer free tasting of crabs, other seafood.

i was there for 2 nights, all via public transport, the electric train. stay near the train station. first evening went to hakodate mountian, next morning the market. 2nd day abit boring but we made our way to goryokaku, nice view from the top. we stayed 2 nights before u got to remember, may is summer, longer daylight. i was there 1st week of aug. so by the time u we see the sunset at hakodate mountain, it was pretty late for us to go for a squid restaurant that was a must go for us. if u are keen for the seafood, i think 2 nights is good. 1 night is insufficient for foods

I think the previous replies to your question would answer your request. I was not there at this time.

Noted an earlier post claimed a 2.00pm close. The following is copied and posted from the website "Travel Hakodate" The Morning Market is open for business from as early as 5 am (6 am during the winter) and closes at noon. Cheers Kayjohn

There's a parking space just opposite the JR station and very close to the market but not sure the fees.