I'm sure you'll get tons of responses from mamas who always choose a sling over a stroller, but if my DD is sleeping and I'm just doing a short in-and-out errand I'll leave her in her carseat and transfer it to the stroller. If I'm doing a longer errand, she'll most likely fall back to sleep in the sling, so I'll transfer her to that.
I also use the stroller in restaurants -- I don't like trying to eat with a baby in my lap, so I'll leave her in the stroller (if she's happy) while I eat and then pick her up.
Places that I wear her are:
*Dropping DS off/picking him up at preschool -- it's great to have my hands free to carry his art projects, snack, etc.
*Children's museum -- the stroller is so hard to maneuver around when it's crowded -- it's nice to be more compact and be able to weave in and out of the crowd easily
*Park -- it's nice to have my hands free to help DS onto the swings, etc., but not have to leave DD by herself in her stroller. Also it's hard to push the stroller on the grass or sand, so she'd have to be quite a ways from us and I wouldn't be comfortable with that
*Grocery store -- DS is still young enough that he usually likes to ride in the cart, so it's handy to be able to wear DD and let DS ride in the cart without having to get a huge double cart or something so that they can both ride in it
*Lately, the pumpkin patch -- again, it's awkward to maneuver a stroller on bumpy ground and in crowds, so wearing her to the pumpkin patch has been nice. Also, the sling doubles as a nursing cover and a blanket for her to lie on if she wants a break
*On fitness walks -- DS rides in a jogging stroller when DH and I go for longer walks, so it's nice to be able to wear DD rather than having to invest in a double stroller. And once DD outgrows the sling, DS will likely be old enough to ride his bike or something and keep up with me and DH
I think once you start just using the sling in certain situations (something small, like a walk around the block), you'll get more and more comfortable with it and start seeing how convenient it'd be to use in more situations.