Down along the Bayfront [1] is a wonderful breakfast haunt, the Coffee House (156 SW Bay Blvd., 541/265-6263, 7 a.m.–5 p.m. daily, $6–12). Scones, muffins, and such creative brunch fare as a wild mushroom omelet, crab cakes Florentine, various crepes, meat pasties, and oysters lightly breaded with Japanese panko breadcrumbs are complemented by well-made espresso drinks. In fair weather, the outside deck is a relaxing spot for soaking up some rays while you gaze out on the harbor.
In the Nye Beach [2] neighborhood, a charming spot for breakfast (including a good breakfast burrito) and lunch sandwiches is Café Stephanie (411 Coast St., 541/265-8082, 7:30 a.m.–3 p.m. daily, $6–8), a bustling cubbyhole with friendly service. Here both breakfast and lunch are served all day long; consider starting your day with a bowl of smoked salmon chowder.
Nearby, the tiny 
Panini Bakery (232 NW Coast St., 541/265-5033, 7 a.m.–7 p.m. Thurs.–Mon., $2–5) is a great spot for a chocolate panini, a ginger scone, a slice of pizza, and the local vibe. It’s the best bakery in town and has a few tables.
Links:
[1] http://www.moon.com/destinations/oregon/central-coast/newport/sights/the-bayfront
[2] http://www.moon.com/destinations/oregon/central-coast/newport/sights/nye-beach