THe only problem with the umbrella strollers is that there's no place to stash your stuff, and if you hang bags off the handles the strollers always tip over. And there's no relief from the sun, a big negative for me!
We have a battleworn graco doublewide stroller (that's narrow enough to fit through all doorways) that we always bring with us. It carries now 50 and 35 lb kids, tons of water, hats, and sunscreen in the basket underneath, and when we are on the monorail or busses we just hop the kids off the stroller, collapse it and trap the stuff inside, and we're off.
We rented a double stroller just once and didn't like the wait to rent, the wait to return, and it wasn't as comfortable as ours. Plus, you can't personalize it like you can your own and you spend ten minutes reading every name on the back of every identical rental stroller trying to find your own.