For breakfast, if you are around on saturday or sunday you should stop by Bouchon Bakery in Yountville for doughnuts, they offer 2 different types (check their facebook page to see which ones are being featured) and there will be a line so be prepared to wait. The chocolate ones are a bit intense, I would recommend one with a fruit filling instead. Also, if any members of your party are too desperate for coffee to wait in the big line, you can always go around the corner to the express window. There is an outdoor seating area, although there are a few too many birds swooping in for crumbs for me to be entirely comfortable. Fridays I like to get my pastry fix at the St. Helena Farmers Market in Crane Park, volunteers staff a table with a selection of baked goods from several different area bakeries. Go early to get the best selection and make sure to check out the bocce players along with the the veggies, fruits and beautiful flowers. If you happen to be in St. Helena mon-thurs you can always grab a delicious english muffin sandwich in the Model Bakery, right on Main Street.
For lunch check out the Oxbow Public Market in Napa, they have arepas that I hear are very authentic. They are a sort of grilled corn cake sandwich, that you can get filled with chicken, beef or beans. They are delicious. If Venezuelan isn't your thing, Oxbow also has restaurants selling oysters, pizzas, tacos, wine, cupcakes and ice cream (and yes I realize wine is not exactly food, but a wine bar serves food, so it counts). If you would rather save your cash for wine tasting, stop by Oxbow on tuesday evenings for locals night when you can take advantage of the specials and save a few dollars, for example at the Oxbow Wine Bar carafes are $2 off and draft beer is $1 off.
Of course I have to mention Taylor's/Gott's (there was some controversy over the name, it's all very dramatic and would make for a good Lifetime movie, officially it's Gott's now, but half the time I still call it Taylor's and the old Taylor's sign still hangs out by the road). There are three now, one in San Francisco, one in the Oxbow Market and the original, in St. Helena. It's a burger place, but since this is the Napa Valley it's a burger place with a wine list and a $1 corkage fee. The milkshakes are worth mentioning (quite delicious) as are the lines (quite long at lunch and dinner but practically nonexistent at 3 or 4 in the afternoon).
We basically only go to one place for dinner, Rutherford Grill. It is known for its smokily delicious meats and while you wait for your table out front (and you will most likely wait, even if you do have a reservation) you will be able to smell why, it smells amazing out there. There is no corkage fee, so we bring a couple bottles of wine (I feel like I should mention this is a family tradition and there are about seven of us drinking said bottles of wine, we don't each drink a few, we aren't that big a family of lushes). You should probably get the cornbread, I hear it has bacon fat in it, do I need to say more? My cousins swear by the ribs, we all love the wild rice salad that is one of the sides, so much so that we got the recipe last year, and I don't think my mother has ever not gotten the chicken dip sandwich, which is technically not on the menu anymore.
This is getting a bit long, so I will wrap it up with a list of my suggestions (and add a few more I didn't mention above) and links where you can find more information and bring you part two later, with my favorite wineries.
For Doughnuts: Bouchon Bakery
For Pastries: St. Helena Farmers Market
For Breakfast Any Day of The Week: Model Bakery
For Burgers: Gott's/Taylor's
For Dinner: Rutherford Grill
For Mexican: Villa Corona