If you are charging admission of any kind it is pretty much out of the question (legally anyway). Now if you were to do a completely free show you can get into a legally grey area. According to the city codes it does include free dances as well but the wording is iffy. You would still probably get shut down but you may win in court but that doesn't do you any good after the fact.
Basically Columbus has the dance hall laws that were created in the 1920's (chapter 555 of the columbus city codes) that was used in the 90's-present to close down all night raves after their hayday. It basically states that you can't have a "public dance" go past 2:30 unless it is on a legal holiday which usually only applies to Sunday nights before a Monday holiday (except the 4th and NYE that can be any day.) Even then you have to get a special permit from the department of public safety. The guys that hosted the Ritual Events did it successfully 4-5 years ago though.
Now the only loophole you have is if you are doing a private event that isn't open to the public. The problem with that is that most houses can't hold the amount you want and you get noise issues and most clubs are going to charge you a ton to actually close the club for you.
I have done a ton of reading on the issue and am very passionate about it. There are really only 4 options for you:
1) Find a "private residence" that isn't in a quite residential neighborhood, so in the middle of now where or on campus are you only real options.
2) Find a bar or club that is normally closed on the day you want to hold the event and talk them into letting you rent it out that late. Most will be pricey if they aren't selling alcohol to you and selling alcohol could be considered "charging" for the party. And most bars/clubs are only closed on really slow nights, Sun-Tues.
3) Find a non-traditional venue that doesn't stay open late. I have tried to talk to a few and most just aren't interested or are too expensive. Not being able to charge anything for admission limits your options (unless you have a big budget). If you are interested in the few places I know of that would consider it PM me and I'll let you know.
4) Hold the party the night BEFORE a holiday (ie after midnight it will be a holiday) and get a permit from the department of public safety and talk a club into letting you hold the party then.