Yom Kippur is the Super Bowl Sunday of Jewish Holidays - even people who aren't regulars or aren't affiliated in any way come to services on Yom Kippur. Which is probably the worst idea - their one exposure to Judaism is a day of fasting, prayer, no sexual activity, no regular shoes, and more boring prayer. Why couldn't everyone come for Simchat Torah instead?
So how can you use this opportunity to give people an interesting and meaningful experience, something that might inspire them to come back again or to explore more about this thing called Judaism?
One idea it to have explanatory services - where prayer is not a boring chore but a chance for people to think, be challenged and to find out what these words are that everyone is [supposed to be] saying. It's hard to run these types of services for all 5 prayers, but try Kol Nidrei Explanatory Services (see this Wiki page for some help), the quintessential Yom Kippur prayer - and the one that people probably understand the least. A discussion and an understanding of the prayers, can bring along interest and attachment to those rituals which can seem so monotenous. For some tips on understanding the day of Yom Kippur as well as how we prepare, check out NJOP's page on how we prepare and celebrate the Yom Kippur holiday.
Another idea is something that can be modeled after an annual event at Penn called YKAP - Yom Kippur Across Penn. After the different services, there are lectures/discussion sessions advertised all over campus - in Hillel, in the Quad, in the LGBT center, etc. They are run by a range of students and faculty and they address a myriad of topics in Judaism, which may or may not relate to Yom Kippur. They draw a lot of people, often people who never engage in Jewish learning but having been inspired by the power of the day, or who saw the intriguing advertising. They only way to find out more is to show up to the event or discussion!