As with most cities and destinations, you will find a few interesting museums here. The Kushiro City Museum is worth a look. It is located on a hill above Lake Haratori, and explores the local natural history. Most exhibits include English descriptions, so you won't be confused or misunderstand what the exhibits are all about. The Kushiro City Zoo will be good fun for your whole family, and it is only a short drive from your Kushiro hotel. One of the more beautiful spots nearby is the Kushiro City Marsh Observatory.
Kushiro is directly linked to Tokyo's Haneda Airport, and a flight is only about 90 minutes one way. You can take an airport shuttle from the airport into the city – the bus schedule matches the inbound and outbound flight schedule ensuring you can always find a bus to take you to town. You may want to seriously consider renting a car at the airport though. Public transportation in Kushiro is very limited, and taxis can get expensive after a while.