Are there any advantages to staying at a disney hotel? What would you recommend to keep the cost down?
There are those that will swear that there are tons, but I am not one of them. My trips tend to be 3-4 day type trips, not long getaways where I would appreciate all that a nice hotel offers (planning to stay at Yacht Club when we finally get back to WDW!). We spend the vast majority of time in the parks, so paying extra for a bed to sleep in doesn't sit well. The Good Neighbor Hotels are literally right across the street from the park plaza in most cases, and those that are a bit further have the ART shuttles that will bring you right to the plaza.
Further, the monorail is experiencing a ton of problems right now, so that benefit has been cut back quite a bit.
Personally, I would recommend you save the extra cash, get a Good Neighbor hotel, and use the savings elsewhere on your trip.
If you want a good place to stay, we usually use Mariott's Anaheim Fairfield or the Radisson Suites, (prefer Fairfield, but nothing wrong with the Radisson).
If you prefer Disney properties, Grand Californian is the best of them, though there is a ton of construction going on right now, and noise might be a factor.