Kochi is a rather large city, but the tram system (Kochi Electric Railway) helps make getting around easier. Kochiekimae Station is located just outside Kochi Station. Trams going in each direction depart from here. You can pay per ride or buy a day pass. The day pass for travel within Kochi city is 500 yen and 800 yen for the full use tram pass which includes travel to Ino and Gomencho.
Harimayabashi Station is where the trams branch off and there are three different Harimayabashi spots (one for each direction) so pay attention to where you are and make sure you're going the direction you want to travel in.
Some of the tram stops of interest:
-Harimayabashi Station: Harimayabashi Bridge
-Kochijomae: Kochi Castle, Kochi Prefectural Museum of Literature
-Kenchomae: Former Yamauchi Samurai Residence, Yamauchi Shrine, Tosa Yamauchi Treasure House
-Kamimachiitchome: Sakamoto Ryoma Birthplace, Roma Birthplace Memorial Museum, Ikemen Ryoma Shop (Nishimura)
-Saenbacho: Yokoyama Ryuichi Manga Museum, Tour boat docks
-Kenritsubijutsukandori: Prefectural Museum of Art
-Sambashidoriyonchome: Kochi Liberty and People's Museum
Kochi is one of Shikoku's largest cities, so it is well connected within Shikoku as well as to the mainland by train.
Kochi Station is its main station. From Matsuyama and Takamatsu, Tadaotsu Station is a common place to change trains to head to Kochi.
From the mainland, there are direct trains to Kochi from Okayama via the Marine Liner. Alternatively, you can take the Marine Liner as far as Sakaide or Takamatsu and then transfer to the local trains (at Tadaotsu or Marugame) to get to Kochi a little cheaper.
You may take a ferry from Kochi New Port (near Katsurahama Beach) to other destinations in Japan.
There are different classes of rooms, ranging from Private Suite w/toilet & shower, Private Room w/toilet & shower (Bunk Beds or Tatami), Shared Bunk Compartments or Shared Tatami Sleeping Space.
There is a rather uncrowded big public bath and Sauna with an Ocean View.
For details and prices (in Japanese):
To go back to Matsuyama from Kochi it is best to take a JR bus which is also included on the aforementioned pass. The bus departs hourly from the bus station near the JR station and takes about 4 hours.
We had a JR Shikoku train pass for 3 days unlimited travel on JR trains and buses. We travelled to Kochi from Takamatsu (via Kotohira and the Oboke/Koboke gorge) by Limited Express train on the JR Dosan line.
Here is a link to a very cool page that lets you see the routing between cities/stations/ports within Japan. It will tell you the route and includes the cost and time. http://www.jorudan.co.jp/english/norikae/.
As Kochi has a big harbour you can take the ferry to many cities of Japan. The over night ferry saves you the money for a night stay and you don't loose a day travelling. I went from Kochi to Osaka. The overnight ferry is also very cheap compaired to other transportations available.