I've been to WDW 13 times and I've stayed at the Dolphin during each of the past five trips, plus several times before that. I've also stayed offsite and at a number of other resort hotels. My mother is a travel agent so we would usually stay anywhere if she had a decent incentive, but without any special deals she generally also defers to the Dolphin. Anyway, I'll be back in November with several first-timers - we considered getting a suite somewhere b/c of our group size but ended up booking several rooms at the Dolphin after they saw my photos from past trips.
The pros for me are (in no specific order):
1.) Price/Value - I have a Starwood corporate membership so I build starpoints and can usually get a comparatively good rate using that, my AAA membership, or whatever promotion they have going on.
2.) Location - I love being able to walk around the World Showcase at night while sampling food and drinks at each pavilion, watch IllumiNations and then walk back to the resort along the Boardwalk. There are often "street performers" out there, plus you can stop in at a number of stores, bars, or restaurants so it's generally a great atmosphere at night (or anytime!). I also like getting up in the morning and being able to either walk or take the boats to Epcot/HS. You can catch the buses to MK/AK right out front - they run frequently and if you catch them at the right time they won't be crowded either. Finally, you can request a balcony that faces Epcot so you can actually sit out there and watch the fireworks - they will charge you a premium for this if you book in advance but I've gotten free upgrades at check-in (which is also an SPG benefit).
3.) Pool - the pool seems more relaxing/less crowded than the other resorts, but that could partially be because I've made the past few trips in Oct./Nov./Dec. It's not as large, and it doesn't have any theming, but our travel party doesn't include children and none of us really mind.
4.) Food - I thought about whether to put this as a pro or con, but ultimately the food has always been good/great so it ended up on the pro side. I've eaten at the Fountain, Cabana Bar, Pikabu and either Fresh/Garden Grove, or maybe both (and I've had drinks at Bluezoo if that counts). On the other hand, there are people that will go to WDW and say "I can't wait to have the Tonga Toast at Kona," or the Kitchen Sink at Beaches & Cream, or whatever else... and for me there's not really a *signature item* (or items) at any of the resort restaurants. I've eaten there because it's convenient and reasonably priced, but not out of any specific desire to eat at those places. However, I've heard Shula's is pretty good so maybe I'll give that a try on the upcoming trip. Anyway, you mentioned that you plan to eat in the parks, so it should be just fine for your purposes!
Cons:
1.) I think they offer a dining plan for the resort restaurants, but it's not the DDP.
2.) No DME - right now I'm looking at spending approx. $300 on a rental car, which will be used to make several trips to/from the airport (travel companions arriving on various dates), and trips into Tampa and Orlando so the cost in my case is justified (I think). Other than that, the car sits in the Dolphin parking lot, which you also have to pay for.
3.) You're truly staying at a Sheraton on the Disney property, compared to a Disney hotel so it's slightly less "magical"... with that being said, I love the "heavenly beds" and the rooms are all very nice, as is the entire resort.
I think that covered your questions on transportation and breakfast as well - as far as breakfast prices, we usually get cereal, fruit or some of the hot menu items and I don't think the price has ever exceeded $10-15. Anyway, let me know if you think of anything else and enjoy your stay!
