BJfly,
I assume you are talking about WDW and not Disneyland. There is a HiIlton directly next to the Anaheim park as well.
The WDW Hilton is a short walk over to Downtown Disey, where you can pick up the shuttle. We traveled with our daughter's stroller without incident, though, if I remember correctly, we had to fold it up every time we got on the bus.
The buses run frequently but the route to the parks takes 20-30 minutes. The hotel was nice enough and staying near DTD was good for food options on days we werent at a park to eat.
OTOH, staying a hotel with monorail access to WDW would be ideal for that park, but not much of a help for the other parks in Disney World.
Bon voyage.