Hello, Tiffany! Thanks for bringing your question to the Disney Parks Moms Panel!
When our daughter was younger, she too would often take naps in her stroller while we were at the parks. If your child happens to doze off around mealtime, most
quick service restaurants can accommodate strollers in their outdoor seating areas. I know that Flo’s V8 Café, Galactic Grill, Red Rose Taverne, Boardwalk Pizza and Pasta, and the entire Pacific Wharf dining area (to name a few) all allow strollers and have plenty of seating so you can hopefully grab a quiet and shady table.
For table service restaurants, you will need to park your stroller outside before entering the restaurant. So if you have a
dining reservation and your little one is still asleep, you will need to carry her inside and most likely wake her for the meal. I remember one of our first trips to the parks when my daughter snoozed all the way through dinner while we held her. So we just got her meal packaged to-go and, of course, she awoke just as we were leaving the restaurant and proclaimed she was hungry! Kids seem to follow their own schedule when at the parks so we always try to go with the flow as much as we can.
I hope this information was useful. Please stop by again if you have any other questions!
-Linda