We stayed here when we first got to Columbus, and Greystone really cares about animals. They allow you to keep 2 pets in your apartment for a deposit fee.\r
They have "Play Areas" including a 100' dog run that is fenced in, so you can have them race around and play fetch without leases. \r
They also have "Poop" recepticles so you don't have to take it back to your apartment. *bonus*\r
Finally, they have dog washing areas and the apartments have sound proof walls, so you can hear your pets, but not your neighbors.\r
I highly recommend using Greystone for apartments if you want landlords that love pets.