I used to have common doves indoors, they are nice pets, relatively trouble free. They just need a decent sized cage, something appropriate for a cockatiel is OK, but a parrot sized cage is better so they can get some exercise. If they tame down, which can be done with a little work, you an let them out for a little supervised exercise in a closed room.
Diamond doves are a nice compromise. A lot smaller than regular domestic doves, very pretty, vocal with a pretty "coo" but they pretty much MUST be kept indoors from what I've read except in the mildest climates. I've got four of them now, but only got them about a month ago.