While a greyhound is a good choice many rescues will not adopt one to a home without a fenced yard or who is not home regularly during the day.

I am a Newfie owner and they are a wonderful breed. I don't live in a huge dwelling and provide her with plenty of exercise. I am also an obedience instructor which plays a lot into her activities. They are very even tempered and such loves BUT when you get a dog of immaculate size, you need to consider several things:
1) Larger dog = more food. I have a Lab and a Newfie and my Newf eats double what my Lab does per day.
2) Grooming can be expensive. I brush her every day or every other day to prevent matting. She is also professionally groomed every 6 weeks, costing around $60 each time. If you don't take good care of their coats, I have seen people with $100 grooming bills.
3) Going to a reputable breeder is imperative. Newfs and other XL breed dogs can suffer from various issues - patella luxation, hip dysplasia, etc. Even going to a reputable breeder does not necessarily deplete the problem.

Basing a dog breed on ability to go off leash is not always the smartest move. Some dogs develop that capability, some never will. Having trained many German Shepherds, I have seen an incredible number that are not able to be off-lead regardless of training. Some dogs will not, in the long run, fit the generalized breed temperament.

Exercising a dog is imperative especially without a fenced yard. Regardless of the breed, I would consider activities like agility or tracking to keep your dog happy. Dogs who are bored can be destructive regardless of the breed.

Some breeds you may want to consider:
ENGLISH Cocker Spaniel (not the American)
Australian Shepherd
Flat-Coated Retriever
Setter family
Collie
Sheltie

No matter what you choose, look into the hidden costs you will need to consume and decide whether or not you can afford the breed generally speaking.