Best breakfast we had on our Costa Rica trip was at Soda de Sirenita in Santa Teresa. Highlight: best banana pancakes ever!. Located near the fork road at Mal Pais and the road into Santa Teresa on the right just past the 2 banks and ice cream shop. It opens before 8am unlike most other breakfast joints in town. Outdoor covered patio area with 4-5 tables.
We also loved Burger Rancho. Yes, they have burgers, but that is only a small part of their local cuisine menu. The sword fish and chicken dinner entrees were great. Another good sign - the locals seem to like the place, too, as we saw as many or more to-go orders going out the front as being served at the tables. Outdoor covered patio with 7-8 tables and free wireless internet access.
Note: Throughout most of rural Costa Rica, nearly all small restaurants are staffed by only 1-3 people - your cook might even be your waiter. Expect service to be slow but the payoff is great food! We loved the food in Costa Rica! Just have a beverage and enjoy the experience.