A backyard doesn't stimulate a dog the same way as a walk does. To a dog, a yard is still just a boring old house. It's nice if you're lazy but it's still best for the dog to take it on long walks. I would only use a yard to actively play/train.
I think that's a huge problem with pet owners, in that they only think of what is convenient for the owner. Owning a pet comes with responsibility...now how much attention does a cat need?
For cats it's really best to have two of a similar age. They will play with each other and will actually in my experience get more friendly with people if there's another cat buddy around. I also make time every day to play with the cats with string/toys/laser pointer/whatever. Cats actually do need attention contrary to popular belief, especially if you don't let them outside (not a good idea in a US city).