You may find this post curious coming from a cat lover, but when I retire (at some point in the future, I hope), and my kitty population is no longer with me, I may be going Greyhound.
There are a lot of misconceptions out there about greyhounds. You don't need to have a house with a football field-sized yard for them, and they aren't constantly on the move. Most greyhounds up for adoption will be retired racers, anywhere from 1 to 5 yrs old, but they are sprinters and don't need as much exercise as you think. They're happy to spend most of their time indoors curled up on the couch or on a big dog bed. They are even good dogs for people who live in apartments or condos, as long as the owner is willing to walk them and give them a run in a dog park a couple of times a week. Another exercise option for them is to take them lure coursing, which allows them to run flat out and is just amazing to watch. Most adoption groups either sponsor lure coursing or could point you to a group that does. These dogs are very sweet tempered and many get along just fine with cats and other small critters. They are also very good with children, although some may need to be restricted to older kids.
Many dog racing tracks euthanize a lot of these beautiful animals just because of their sheer numbers, particularly after the racing season ends. This is such a tragedy, and so unnecessary. Unless dog racing is outlawed these dogs will continue to be bred only to race a short time and then be put down. If you are interested in adopting a dog, please look into one of these sweet animals. There are many organizations out there who round up dogs from these tracks and find families to adopt them. I would suggest also that you consider adopting more than one -- they're used to being around a lot of dogs and they're like potato chips anyway!
I have added a couple of links to Greyhound adoption organizations in North Carolina. You can Google for some in your own area.