Actually, the water in RI is very good.
We don't buy soda and the kids never have it (only at parties, they might have a small cup).
The grocery bill killers are meat/chicken/fish and milk (lots!)/cereal, etc.
From the days of my first job working for the family institutional grocery wholesale firm, the ratio that restaurants, hospitals, schools, etc. usually attained in a 'plate cost' was the standard 80:20 or 80% of the meal cost was in the entree, 20% in everything else, the sides - potato, rice, other starch, vegetable. Examples:
1) 'Meat' - your main cost; so we'll start there
We cut our bill considerably by purchasing family packs of fresh boneless, skinless chicken breasts (!) which we can get on sale here for $1.99/lb. We buy the largest portions we can get; I split them, and freeze a meals worth in ziplocks. By getting 16-20oz breasts, I can get 4 portions from each, because I split each 8-10 oz half again. That works to $.50-$.63 per portion. I can't do that with canned tuna even.
2) Another meat - boneless whole pork loin (not tenderloin) - same deal as above at even lesser cost. Cutting them is easy, bags are cheap.
3) Beef - my favorite - is expensive. We don't eat it very often. When we do, I don't buy NY Strips or Ribeyes,
but chuck cuts. Ground beef only if making beef burritos or Greek dishes requiring it.
4) Fish - got to shop for the deal.
6) Other protein sources : Lentils, beans, eggs, bulk cheeses.
With something like 208 fast days, we've got the meat dollars under control, but I know with young ones you can't cook as we can in our 50s.
Milk is expensive now. But the stuff it usually goes on is even more outrageous. Breakfast cereals are very costly. Consider old fashioned alternatives - oatmeal, farina. On weekends, if you have time, homemade pancakes are cheap and the kids should love 'em and the fun of making them.
Snacks - a stealth attacker of the food budget, at least here in the Aristokles home. Popcorn is now the preferred (my chocolate yogurt pudding notwithstanding) snack.
We get a lot of stuff from Sam's Club - my source of decent feta, fish, condiments in quantity. A gallon of mayo there is $4.68 here and lasts a long time in fridge. How much is a quart of Hellman's up there?
Wish I could think of more suggestions , but I'm hungry now...