I was elected president of my college’s Pre-Health club for the upcoming school year. I’m trying to brainstorm possible events and activities and was wondering if anyone had any experience or suggestions. The membership of this club ranges between 50 - 100 students each school year, so keep that in mind with your advice 
Some of the stuff the pre-health clubs do at my school: Guest speakers (Doctors, nurses, dentists, allied health professions, public health people, people doing medical research, minorities in medicine, people who work in hospitals, clinics, private practice, etc. Even though everyone is pre-health, different topics still appeal to different people. It would also expose people to different areas of health).
Also, some groups will have many small community service events (maybe with the same place every month for a week) that different people can sign up for and do one day. Networking dinners with med students. Going to schools and giving some kind of health presentation / mentoring. Making a premed blog. Having different drives and fundraisers for charities. Tours of various med schools / hospitals. Events that teach various skills (how to get shadowing, letters of recommendation, write a personal statement, etc.). A panel of upperclassmen in the club to teach the newer members things they wish they had known earlier.
And then the usual club bonding activities, like movie screenings (I guess health-related, or have people vote), cookouts and other dinners just to get to know each other, game nights, trivia, team-based competitions, make your own [craft, dessert, etc.].
Honestly, I’d stick to the academic stuff. Go to hospitals, see if you can go in the ER/OR, have guest speakers, stuff like that.