I posted previously about trying to decide whether or not to get a greyhound, then I decided to get a whippet, and after months of looking for a suitable one to rehome, I took DD(5) to meet some greyhounds, and we ended up adopting a lovely black girl who arrived yesterday 
So far she's great. We were advised by the rehoming people to ignore her as much as possible apart from food, toilet breaks and walks, so she settles herself in without getting so attached she gets separation anxiety when we're not here.
She's had a couple of accidents - one wee near the back door which was my fault as I was cooking and not paying enough attention to her, and one in the night, but she chose the kitchen tiles rather than the rug so she did the best she could 
I know I'm now a bit paranoid about getting her to go outside, but I also know that she's used to not going outside all the time, so I'm trying to balance it.
So, wise dog people, as the weather is nice right now, should I just leave the door open and let her go in and out as she chooses? Or am I setting myself up for trouble that way, on the days when that can't happen?