Cvillecpm, thanks for the web site. Anything that makes it easier to advertise and list units makes me smile! Especially if it's cheap (or free!)

Mr. Nice. The OP doesn't say how long he has left in the lease, only that he left over 2 months ago (and still apparently has time left on that lease!) If he had a long lease (1-2 yrs) and has considerable time left, the LL may end up with a replacement for only the remainder of his lease period. The costs to advertise now may have to be repeated at the end of his lease (when the LL would have normally expected them to have been incurred). So the advertising costs now would be in addition to those he later expects. These costs would be additional costs he would not have incurred had the OP honored his agreement. He owes these cost.
To the OP, to keep these costs as low as possible, I suggest you atempt to find a new tenant for your own unit. Check with the LL, but I doubt he would object. Network with friends and let them know the unit is available. Place an ad in an employee newsletter or bulletin board. Post fliers about the unit at landromats, stores, and banks. The sooner another tenant gets in that unit, the fewer costs you owe.