Muroran, located in southern Hokkaido, is not hard to reach from Sapporo and its airport.
Take a look here about how to get to Muroran, and how to get around it.
Getting to Muroran
Using Limited Express Trains
From Sapporo Central Station, take a Super Hokuto, or a Suzuran limited express train, and in about an hour and a half you will arrive at Higashi-Muroran Station.
From here, to get to the city center, take a local train to Muroran terminal for around 15 minutes. In total it should take less than 2 hours, and the price is around 5000 yen (which is included, if you have the Japan Rail Pass or the Hokkaido Pass).
Using local trains
If you use the Seishun 18 kippu, or you do not plan to use the Japan Rail Pass and you want to save money, you can use local trains, but travel times can exceed 4 hours. Also you will likely need to change train at Tomakomai Station and once again at Higashi-Muroran.
Using bus
Highway buses are available from Sapporo, with Dōnan Bus or Chūō Bus. Approximately one bus per hour for two and a half hours from Sapporo to Muroran city hall (located in the peninsular zone).
PDF timetable (Japanese): LINK
Using Limited Express Trains
From the airport railway station, take an Airport Rapid to Sapporo or Otaru, and get off at Minami-Chitose, the next station. Change here, by taking a Super Hokuto or Suzuran train (see “Sapporo tab”) for Muroran.
Using local trains
Likewise, reach Minami-Chitose first, and continue towards Tomakomai / Muroran. From Tomakomai, local trains are few, so check the timetable!
Muroran can be a pleasant destination to break the long journey from Hakodate to Sapporo. With a Limited Express train (Super Hokuto) it will take about 2 hours and 10 minutes from Hakodate to Higashi-Muroran, where you will then change with a local train for more 15 minutes to Muroran city.
Getting around within Muroran
The city of Muroran is particularly extensive, and basically has two cores: the port area, enveloping Mount Sokuryō-zan (a hill of about 200 meters placed at the center of the city, covered by weather antennas and transmitters, which name the hill itself: sokuryō (測量) in Japanese means “measurement”) and the most recent part, which extends eastwards from Higashi-Muroran station.
During this visit, we focused on the peninsular part, the richest of naturalistic spots. Once you reach Muroran Station, the terminus, you have a compact network of city buses at your disposal. At the tourist information center you can ask for a daily bus ticket (there is almost no information on the internet, not even in Japanese), which will allow you to move quickly along the longer routes.
Although we used the bus during the journey, many areas, especially along the cliffs to the south, are not covered by public transportation, so you will have to walk a lot (and there are several ups and downs). At the end of the first day, looking at the pedometer of our smartphone, we had done something like 45 thousand steps! Bring comfy sneakers!