You may have a sales office on the premises. If they are selling the units, they are probably renting them out. You did not state your location downtown but that would be my first course of action.
I would also ask an agent to list the rental on the MLS, great exposure. They can also place a lockbox on the unit to allow more agents to preview the unit.
Craig's List is great, I have had excellent luck with the service.
The best suggestion that I can make no matter which way you go is to stage it, make it look great, trendy, modern, no clutter. Take fabulous pictures with plenty of light.
Catherine Kolodin, GRI
Offer one months free rent.
Offer maid service.
Offer free utilities
Offer a free weekend in Vegas.
adjust you monthly rent accordingly to the extra expense, or at least compensate some of the additional cost.
Or the time test true favorite..............Lower the rent.
Flyer's Local offices/business in 10 minute walking distance
Keep ads on Craigs List short and quippy......include as many photos as you can. Respond to e-mails Immediately. Good luck!
Obviously, a property management company or experienced REALTOR is the logical step. If you are opposed to that, Craigslist, AZCentral.com, rentalclick.com, etc will give you decent exposure. Can your designated statutory agent help you with posting flyers at the downtown ASU campus?