Have never gone anywhere for breakfast, but I know Mulligans in Sebastian offers breakfast on the river. I don't know how it is, but the rest of their food is good.
I always take at least one morning to head over to Country Ham 'N Egg on US1 in Sebastian. They're nothing fancy, but they're the closest thing I can find to the diner breakfasts I grew up on in NJ. Prices are reasonable and portions seem generous to me.
Two years ago I found a shop on the beach North of DVB. It was walking distance. They sold breakfast plates. I forget what they offered but I plan to check it out next time. It was to late to try it last trip.