I've been one of the co-chairs of my school's LGBTQ group -- here are some of the kinds of things we've done:
- March in the local Pride parade: we wear white coats and hand out apples!
- Outreach with admissions: in early spring we do a phone bank to call admitted students who have identified themselves as LGBTQ on their applications, and we've done an informal coffee shop meet-up at the end of the admitted students visit day
- Workshops on trans health: this is an area where you can collaborate with local LGBTQ organizations if there isn't anyone in your group who feels knowledgeable enough to lead a workshop
- Working with our school to encorporate more LGBTQ content into the curriculum, improve the way that they teach sexual history taking, advocate for pronouns on nametags, etc.
- We usually have a small potluck/gathering around December, and again toward the end of the school year
If Seton Hall has other LGBTQ groups or an LGBTQ center on campus, you might reach out to them to see how you can collaborate or share resources with them.
All that said, I think the most important thing for any new student group is to set reasonable goals, identify and train your future leadership early, and document everything you do (so that no one has to reinvent the wheel later on). It's less important to do a lot of stuff right away, and more important to leave a good foundation for the group to expand in the future.
(omg, how many times can I use the acronym LGBTQ in this post??)