Based on budget (or lack thereof) I tend to stick with the same places visit after visit. Unfortunately, I just can't afford some of the places that I'd like to try.
Since I'm a fan of traditional diner breakfasts, I enjoy Country Ham N Egg restaurant in Sebastian (US1, northbound side, just south of 512) with JP Matty being another decent (and inexpensive) option. Nothing fancy, not necessarily healthy but certainly yummy.
Last visit one of the Front Desk CMs recommended Vittorio's Pizzaria and I have to say they had some of the best pizza I've tasted in Florida, plus excellent service. You could tell they have lots of regulars. It is an old school strip mall pizzaria like the ones I grew up with in central NJ. They have 3 locations, the closest to the resort is on US1, southbound side, in the same plaza as the Publix.
We did the Early Dining Special at Avanzare in downtown Vero a couple trips back and while I had an issue with some burnt garlic infecting everything on my plate, my friend really enjoyed his meal. Based on other reviews, it could be worth a trip.
We also tried Johnny D's Bistro & Market on A1A and they were very good. We took advantage of their Prixe Fixe menu during off season and it was a terrific value for some very good food.
Then there are the old standards - Mr. Manatee's for fried seafood, Squid Lips (darn that evil and delicious bimini bread), Captain Hiram's for burgers out at the Sand Bar while being entertained by a good local band.