If you're looking for a quiet and romantic breakfast, there aren't many options.
I would avoid character breakfasts, as those will always be louder. I would check out Grand Floridian Cafe and maybe The Wave, but I can't comment on the food since I haven't eaten at either one of those places. I know Kouzzina serves breakfast, but that place is super noisy!
Kona gets a lot of good breakfast reviews, but I've eaten dinner there and because the restaurant is very open to the lobby, it can be quite loud.
Where are you staying? If you're at CSR or a deluxe resort, the best option for quiet and romatic would probably be room service.
If you decide you just want good food in a fun atmosphere, and can save quiet and romantic for a dinner, I would highly suggest Crystal Palace or Cape May Cafe.
Both are character buffet breakfast, but there's nothing wrong with 2 adults going. I've done it several times with parties of just adults and we have a great time. Characters are usually good at reading how much interaction you want. The reason I suggest these places is mostly because I think the food is really yummy! Cape May is a bit quieter than Crystal Palace, and also much easier to get an ADR for. Also, if you book a time that is right when they begin serving or closer to the end of the breakfast hours, the restaurant will not be as full and thus less crowded and not as noisy.