If you have the time, buy a stroller at a yard sale before you go and use that one instead of renting. I bought a stroller for $1!!!! We plan on just leaving it behind, either at the hotel or at the airport.
I would advise you to bring your own stroller along, even an umbrella stroller. I found that when we went on our trip, the time that we really needed the stroller the most was at night after the fireworks when it was time to head back to the hotel- that was when our kids conked out and needed to sit while we made our way (with the hugh crowds of people leaving the parks) back to the buses. We noticed many parents carrying sleeping children trying not to jostle them as they were waiting in the lines for the transportation back to the resorts.If you rent a stroller, you need to give it back as you leave the park-IMO you will be very happy to have your own stroller .
Go to www.wdwig.com/strol_faq.htm and you will find lots of info on strollers including pictures of the strollers at each park and comments from people about whether to rent or not to rent.