We've used a stroller every time, since our (petite) daughter has been on board, and she will turn 8 while we are there in July. First time, she was 5-1/2, and we initially did not go with the stroller. After a day and a half of carrying her a good bit of the time, we rented a "buggy" ("strollers" are for babies, but it's OK for a big kid to ride in a "buggy") and never looked back.
IMO, a stroller will greatly increase your child's "staying power" and, thus, yours also. He/she will be able to go longer, do more, and be less crabby...and so will you! Also, as ours demonstrated on several occasions, when they get tired, they simply zonk out in the "buggy". Mrs. YEKCIM and I had a very nice evening at Eppacot after the little YEKCIM-ette did just that. We toured, she slept, and we all had a nice time.
Oh, and just fyi, the YEKCIM-ette *will* have a stroller at her disposal for our 7 day visit next month. We've already planned to get a multi-day pass. She probably won't ride as much as last time, but when she gets tired, she can ride...in the shade.
~YEKCIM