Believe it or not, a greyhound can do great in an apartment. Just give them a nice daily walk and a sizable couch and they are fine. Greys are perfectly happy lying upside down on the couch for many hours a day, presumably dreaming of chasing prey. They really don't need a lot of exercise.

Of course, if you have cats, they greyhound will get plenty of exercise, but you won't have cats anymore. :-(