Don't take this trip if you want to eat well. Instead, go take a trip in France. Seriously, you can get the calories you need, but this trip isn't about eating well. I don't mean this as a complaint, it's just the nature of the trip. Also, don't underestimate the amount of calories you will need. We ate constantly and both of us lost weight even though we are both light-weights to begin with.
Bigger towns (>1000 people) usually had a reasonable grocery store. Smaller towns have limited, sometimes very limited stores,often in the form of gas-station convenience shops selling mostly sugar, salt and trans fats. We ate several memorably good restaurant meals, but most restaurant/cafe meals were of the steak or hamburger and fries or baked potato variety.
We didn't carry a stove, which served us very well. We don't like the hassle of cooking, and we like to be able to easily eat in the tent when it's raining, and we can easily get all the nutrition we need without cooking. If you like the aesthetics of a hot meal, then carry the extra weight and bulk of a stove and pot and fuel, and cook. But you don't need to do it if you don't care about the hot meals.
Our staples were as follows:
breakfast: yogurt (available at 80% of stores), dry and fresh fruit, bars and/or muffins/donuts, sometimes juice
snacks: bars (Clif/Luna/Balance/Power/etc). We were nearly always able to get some brand of bars that had protein. On two or three occasions during the entire trip the only bars available were Quaker Granola bars, which have no protein and which we avoided when possible.
lunch and dinner: crackers, cheese, beef jerky, canned tuna or chicken, fried chicken (available as take-out from mid-sized grocery stores and from cafes), carrots, nuts, dry and fresh fruit, chocolate, potato and corn chips, cookies, salsa, and hummus (available only in larger towns).
The most frustrating thing about the food selection was produce. Carrots were the only vegetable that was regularly available that works well without cooking, and we ate a LOT of carrots - as in every lunch and every dinner on the whole trip. On good days we also got red peppers, a treat. In terms of fresh fruit, the selection was often limited to bananas and apples.
Many people mail themselves food so they can get what they want. For us, we liked the freedom of not worrying about what time and day we arrived at a particular town. While I've said the food was generally pretty uninspiring, that was not an important part of the trip for us, and we chose the freedom of having no worries about arriving in a town in time to get to the post office. If you DO decide to mail yourself packages, then seriously consider arranging with RV parks or motels so that you can pick up your packages on Sundays or evenings. That requires more work up front to call in advance, but you can then have confidence in your ability to retrieve your package. If you arrive at an RV park mid day and don't want to spend the night, you can still pick up your package, do your laundry there, and pay for showers before moving on.