Our diaper bag was stolen once! All that was in it was diapers, wipes and the baby necessities but let me tell you, we were miserable! You really can not live without diapers and we only had luck with just one brand not leaking and no spare clothes either-ugh!
After that, we always left just a few diapers and wipes in the stroller in a zip lock bag that was see through for quick changes and used fanny packs for everything else. We would get a locker and put the rest of the diapers in it along with spare baby clothes, sweatshirts, food, and anything else we needed and then periodically stop back at the lockers when we needed to refill supplies.
I would never leave anything in the stroller, we've even had balloons ripped off the handles. Worse than that, I've seen other toddlers grabbing and sucking on other kids drinks that were left in the stroller-yuk!! Then when their mom calls, they throw them down into the wrong stroller.