ds went to the world when he was 2 months shy of 4 and we took a stroller (we got one of those $30 jeep umbrella strollers) and he sat it in towards the end of the day a lot, and he also used for seat during parades! It didnt have a basket, but I hooked my messenger bag on the back of it, and if he wasn't sitting in it (stabilizing it) I'd just sling it up into the seat. (I was also 5 months along with dd, and it was very hot, and so I kinda needed the stroller as a crutch almost LOL!!)
Dd will be a few months shy of 4 on our next trip and she will DEFINITELY use a stroller, I'd guess 75% of the time. She's quite the diva and sweats easily so I'm sure of that percentage LOL! She is also still a napper whereas DS was 99% not a napper at this age, so the stroller will come in handy then as well. I recently got a new stroller for her because she didn't really need the full sized stroller we have (fisher price safe voyage stroller)... I got the Uppa Baby GLite (
www.uppababy.com $99) and it's an awesome stroller! Dh and I are both comfy pushing - I'm 5 feet, and he's 5'10" - it has a tiny basket, better than none, no parent tray but has a cupholder (that i haven't put on yet), and it is pretty stable w/out her sitting in it and my messenger bag hanging on the back.
HTH some. LOL!
eta - I meant to mention that at that age we'd usually park the stroller at a stroller stop and go do a bunch of stuff then come get it again -- like park @ stroller pkg down near small world, do the fantasy land stuff then go back and get it. Unlike when they're smaller and we'd ride the stroller to most rides/attractions.