My University (SJSU) has a Korean Entertainment club, they have several subgroups to the group. Since there are people that are interested in different things, they have some people tha do dance covers of K-pop songs(they often upload their covers to YouTube), others are part of the singing group (where they cover k-pop songs as well).
They also do a "Family/Fraternity/Sorority" type of thing, where the members seperate into subgroups, and the members are able to have Sunbaes or dongsaengs.
As to other activities they do a Running Man type of thing, in which members who are in the club and people who are not, can do nametag elimination (like in the Variety Show "Running Man"). They also do Karaoke nights, they go to a karaoke place and sing or just chat with others as a way of bonding.
These are just some of the things the club at my University does, I hope it helps! (^_^) the ideas from others sound great too!