This is what I carry around with me, since Ben became a toddler.
My bag is by Summer, I got mine from Amazon.
This is pretty self explanatory nappies, wipes, changing mat, nappy bags and hand sanitiser. I always make sure I use our own changing mat, over the top even if there's already one there. As only Ben has used ours and we wipe it down, just more sanitary.
I always carry Ben's red book around - you never know what could happen! And also some sachets of Teetha for emergency's. If Ben has been having a rough few days I also try to remember to pop some Calpol in the bag as well.
These are my things, purse, phone, keys, sunglasses, and the lip product that I'm wearing that day - if any.
Since Ben started walking I keep the reins in the changing bag. Sometime's I'll let him out to have a little walk around, and he doesn't really like holding my hand much any more.
As we seemed to have an unusually sunny Summer this year I just kept Ben's suncream, sunglasses and hat in the bag. Right now as it's finally cooled down these things aren't in there any more. But will be replaced by his Winter hat and mittens when it gets colder.
Whenever we go out I put in a fresh cup of water, and some snacks, a bib and a muslin cloth for wiping off crumbs (saves on those baby wipes, haha!)