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.
Gregory
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.
5) TURKEY.
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.
Other considerations:
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...