If you are nature person, you can go to Corum's Catak Natural Park which is surrounded with larch trees. Best time to visit the park is between May and October.
Also Corum is best known with its delicious roasted chickpeas (leblebi). There are so many flavors to choose from, chickpeas covered with chocolate, or vanilla, or sesame, or just plain.
In the center city, there is a big range of cafes and restaurants, but one should look for a restaurant that has the popular dish called "Corum Mantisi". Manti is a Turkish dish which is similar to ravioli, but instead of cheese, it is stuffed with beef. Corum is the city that has the best recipe for this dish.