Greyhounds are actually a wonderful breed and, personally, I would recommend them to anyone. I had two greyhounds (at different times) growing up and they were excellent pets. They do enjoying getting outside to run laps but they are pretty low-key dogs and are not hyper. They do love attention, but that can be said about most dogs and most greyhounds will just go lay down if they aren't being given attention. They managed just fine here in the Houston heat & humidity, but of course you need to keep them hydrated like any other breed. Although they are short-haired dogs, they do shed and you'll want to brush them periodically, but it's quite manageable. One characteristic that always stood out to me is that they are pretty schedule-driven dogs. They have an incredible internal clock and if you get them on a schedule in terms of when you'll be home, when they are supposed to be fed, walked, etc., then they'll expect to stick by it. That's not to say that they can't manage long days if you're going to be gone for a while. We were able to leave them at home for a ~12-hour day if we had to make a day trip somewhere and they were perfectly fine, but I'd say that would be the maximum amount of time to leave them alone without someone letting them outside. In regards to the gas issue that blondetall mentioned above, it's true, but we also found that only giving them a certain type or brand of dry dog food helped prevent that. We only fed our dogs once a day (as opposed to always leaving a bowl out) and they were perfectly fine and healthy.
Overall though, they are pretty low-maintenance pets, in my opinion. Greyhounds are incredibly sweet dogs and are extremely loving. They do not lick and they seldom ever bark. They are very quiet and sleep a lot so it's not like you have to keep them entertained constantly. The only time they might slobber is when they're eating. Otherwise, they don't slobber at all.
I sincerely miss our greyhounds and when the time comes that I want to get another dog, it will likely be a greyhound. There are so many of them that need good homes when they are retired from racing and forgotten about. Honestly, I think they serve a much greater purpose and get a lot more out of life as pets than they do as race dogs. They are usually retired when they are only 2-3 years old and on average they live to be 11-12 years so they have a ton of life and enjoyment left after retirement.
So if you like Italian greyhounds but want a larger, less hyper, and less fragile version, then I would go with a greyhound.