Kochi is a great city.
Some other places worth considering:
IN KOCHI CITY:
-Sakamoto Ryoma Birthplace Museum (they have an English audio guide that you can use, so you can actually learn from the museum). This area also has the marker of Ryoma's actual birthplace, the Ryoma Post Office, and other sites related to him.
-Former Yamauchi Samurai Residence - It's an important cultural property and surprisingly free. The Yamauchi Family Treasures Museum is nearby as well.
-Katsurahama is mostly for the view of the ocean. I actually disagree that the Tosa Dog Center is not worth it. I think it depends on your personal views on dog fighting, but the dog fights are an interesting part of Kochi's culture/history. The Tosa dogs were bred specifically for this purpose, so dog fighting is the only reason they exist at all. If you are interested, make sure you find out what time they will be held the day you will visit.
OUTSIDE KOCHI CITY:
-Ryugado Cave, This is a really interesting cave. To get the most out of it, you may want to purchase the small book at the visitor center upon arrival prior to going up to the cave. It has English descriptions and is a good way to make sure you don't miss any of the interesting features.
-Aki city: Nice for walking or bike riding (bike rentals are free). It's a former castle town with some remaining buildings, a famous clock tower, and the former home of Iwasaki Yataro, the founder of Mitsubishi
-Kitagawa town: A town famous for its Monet garden and Nakaoka Shintaro, friend and ally of Sakamoto Ryoma who was fatally wounded in the same attack that killed Ryoma.
-Ekingura: This is a museum in Konan about a specific type of art:
http://www.ekingura.com/The west part of the prefecture is dominated by the famous Shimanto River. There are bike rentals in the area if you prefer to see some nature.
The two tips of the prefecture (Muroto and Ashizuri) are famous for their lighthouses and ocean views. Ashizuri appears to be more interesting, but I haven't been to either and they probably take too much time to reach to make it worth it for a two-day trip.
As for food, whale is also famous in Kochi. The famous area for whale is the eastern portion however, the restaurant Suigei-tei in Kochi city is famous for the whale in the region.
For Katsuo no Tataki, two of the famous places are: Issyun and Fujinoya, but there are many other places that serve it.