I haven't eaten at Cosmic Rays or Casey's Corner in forever and a day (or within memory) so I'll let others talk about those locations.
I think it really depends on what type of food you're looking for will held determine where you might go. Please note, that for Be Our Guest, you will need an ADR no matter what, even for lunch.
In terms of atmosphere I would rate them as follows:
Be Our Guest
Columbia Harbor House (upstairs)
Pecos Bill
Pinocchio Village Haus
I personally find it hard to rate the food, because again it really depends on what type of food you're craving that day. Though Pinocchio would probably rate last.
Be Our Guest - French Influenced American food. This location is unique because you order and pay and then the food is brought out to you via magical rose/magic band rfid. The food is generally good and served on real plates and silverware. I've enjoyed the turkey sandwich multiple times and enjoyed it each time. I personally don't care for the cupcakes here, but others love them. It doesn't always feel like quick service, but the portions are a bit small in my humble opinion.
Columbia Harbor House - This is primarily seafood and 'New England' fare, much of it fried. They also serve some healthier items in terms of salmon, a veggie sandwich, and steamed broccoli as a side. I've enjoyed the lobster roll, fried shrimp, and macaroni and cheese (either with lobster or shrimp, I can't quite remember). I enjoy eating here, especially on the second floor where it's quieter and the seats have backs, which wouldn't seem like a big deal, but after a long day in the parks that is very welcome. I find the portions filling and I appreciate having the broccoli over fries.
Pecos Bill - Within the last year to 18 months they have undergone a menu change. It's now much more Tex-Mex inspired food with a popular toppings bar. The portions are large here and could probably be split between people depending on how big an appetite you have. The amount of food is expanded with the toppings bar, which from my memory includes lettuce, tomato, onions, cheese, sour cream, guacamole, mushrooms, peppers, and salsa. I used to always get the taco salad, but that has since been removed from the menu. The last time I was there I had the chicken fajita platter. Maybe a few more items. I was pleasantly surprised. I did not walk away hungry from here.
Pinocchio - Italian inspired American food. Of the four, I would probably rate this the lowest. It can get incredibly busy and crowded, which greatly detracted from the atmosphere. The flatbreads aren't bad, I think I had a margarita (tomato, basil, and mozzarella) flatbread, which wasn't bad, but not outstanding or particularly memorable.
Again, my recommendation would be to look at the menus for the restaurants (either here, on Disney's website, or allears.net) and decide which might be the most attractive for you to eat at. Be Our Guest is a great experience, but if you're looking for the flexibility of Quick Service that might not be the best choice for you.