I don't think there is a "rule" about this... whenever you feel comfortable doing it. There will always be somebody who is going to judge your parenting decisions based on stupid crap, just do what you think is right.
We went out for a walk in the neighborhood with the stroller at 5 days, our pediatrician encouraged it. At three weeks I started taking her shopping and on errands in the stroller, but always covered up. Agree with PP, it's whatever you are comfortable doing.
We went hiking at 11 days. I desperately needed out of the house and it had been cold and rainy since she was born. It was free national park week, so we went hiking. It has been rainy and cold since that day. Today, though, is beautiful and we are so going out again. She's 3 weeks.
We've been taking daily trips out of the house since he was 6 days old. I can't stand to be in the house all day so we usually go somewhere each day (Target, supermarket, mom's group, etc). We also go on walks when it's nice (our weather has been weird). I need it for my sanity.
We went to Costco at 12 days. We walk around everywhere... I just don't let people touch him... Keep him covered... But he doesn't like it when it's breezy out.
We take DD out almost every day. Usually close to home (brunch, church, just out for a walk). We have taken her to the mall and Target. I started when she was 3 or 4 days old. She is always covered up. She likes being outside and I get cabin fever.
We just took our almost 3 week olds out today. We would have gone earlier but it has been cold and rainy and I was having a hard time walking around post c-section.
We also went on short errands and trips outside the house very shortly after coming home from the hospital. I would go insane having to stay in the house. Totally up to you!
My son is now 3 weeks and we've been out a few times. We went to my oldest son's soccer game at 5 days old. With the nice weather it was encouraged for us to take him out which is great because I hate to stay indoors. We keep him covered and don't let ppl around him and he's done so well in his car seat
We walked our first day home and everyday after that. (We live in a city on a carfree street so we didn't have a choice even if we had wanted to wait.)
Re: When is it appropriate to take you baby on a walk? Not necessarily a public place.