It's a bit different for me as I've always had rubbish sight and am fairly confident about being out on my own. I lost a lot of confidence once I had dd though. I was terrified about crossing roads and have only started using a symbol cane since I had to take her out. When I first had her I lived in London, 200 miles from family and friends with dc's and DH worked long hours. I HAD to do things on my own. But we moved up north while she was a baby and I have support now. I still sometimes carry dd across roads so I can really concentrate on the traffic and run if I think I need to. She's 6 so I really have to stop doing this! (she's going to get eaten alive if the girls in her class see us)
But if I'm going out with dd on my own I will only go to places I know really well. Particularly I have to know where the nearest toilet is at any given moment as dd only ever gives me 30 seconds notice!
If its a busy place dd HAS to hold my hand all the time. Otherwise I can't concentrate on finding my way around because I'm worried about where she is. We had a phase where this was a problem (and suspect we are heading for another one) but that's the condition of us being out together and if she won't I call a taxi and we go home.
I had some mobility training when I moved to help me get to know my new area and routes that I could take a buggy down safely. (but until dd was 3 I mainly used a selection of slings)
Now I only really panic if I have to take one of dd's friends anywhere, especially if I have to cross a road, the responsibility of keeping your own child safe is pretty daunting but it's nothing compared to having responsibility for someone else's!
I'm glad this thread is helping you. I talked to wannabe when I was either pregnant or dd was tiny, can't remember, but i remember thinking how reassuring it was that she was coping so well.