There is plenty of food available on STJ, so it's certainly not necessary to bring food in order to eat. There are markets, which will be more expensive than on the mainland. Some folks bring a good bit of food along either to insure good quality, to have favorite foods or brands or to save a bit of money. We usually bring coffee, granola and some peanut butter, jelly and bread. We consider those emergency rations. The rest we buy there.

If there is something specific your daughters enjoy or live on, I would consider bringing that. As Nick said, most things are more expensive in general but we found cereals much more expensive (my kids require cereals) and were glad to bring some frozen meats where we could save on bulk. Had trouble finding certain spices or season mixes so if you have favorites, bring them as well and leave what's left for the next group.
Just be prepared to spend a little more for milk, veg, etc. than you are used to but certainly not enough to crush expenses on the trip.

We just got back - me and my two adult kids. We stayed in Maho Campground. I packed all essentials in a carryon and checked a bag with food and other extras, such as extra towels and a neat sheet (which would be a great thing to have with kids!). I took granola bars, Payday candy bars, honey roasted nuts, crackers, breakfast bars, and other snack items (but nothing chocolate that would melt in the heat) that are much cheaper at home. I took everything out of bulky packages and packed inside two small collapsible coolers inside a suitcase. For example, a box of Poptarts at the Maho store is $4.50. It worked out great. We ate out of food we brought along for almost every breakfast and lunch, and then went out to dinner. It helped keep the food budget within reason and was really convenient.

We travel light, with just carry-on bags, but we still brought "staples". For the two of us, we packed a plastic freezer bag with enough bite-size shredded wheat for 6 days, a box of generic Wal-Mart pop-tarts, a plastic bag with enough ground coffee for six days, a box of individually-wrapped peanut-butter crackers, and a box of individually-wrapped granola bars.This allowed us to have breakfast in our apartment and liberated us from having to be near food at lunch time. When we arrived we stopped at the Starfish market, which is a nicely-stocked grocery store. No, it's not a Super Wal-mart, but it had everything we needed. Yes, the prices are a bit more than the mainland grocery stores, but sheesh, everything has to come over 1,000 miles of ocean to get there! It's funny what people will complain about. We were standing in the check-out lane at the Starfish listening to the couple in fron of us. In one breath, the guy told his wife that he'd gotten a "good deal" on the villa they were staying in, because it was only $2500 a week, and in the next breath his wife complained that Ritz crackers were over $4 a box! Gimme a break!

Depending on where you're staying, you might want to bring kleenex and other papergoods too. I never checked the store prices but I'll bet those weren't cheap. We also brought instant coffee as we stayed this past trip at Concordia where there currently is no store or restaurant-nasty stuff but if you need a hot drink fix in the early AM and don't want to travel and/or don't have a coffee maker....We also packed sugar and creamer packets rather than buy a large container of suger for example. Do NOT bring marshmellow fluff unless you have a fridge. We brought that to Maho one year and the heat made the fluff seep out over the top of the jar- very messy! Just keep the heat in mind and plan to fridge almost everything to keep it eatable. There are some earlier threads about bringing food, mostly about packing and bringing frozen meat if I recall correctly, so search away!

Another option is to pick up a few things on STT en route to heading over to STJ. Pueblo supermarket (sub-base), Cost-U-Less warehouse store (Weymouth Rhymer Highway) and KMart (Tutu Park Mall) are all on the way to the STJ ferry, are less expensive than the STJ stores and if you're going by taxi the driver will usually accomodate you by making a stop if you find the right one. Most St. Johnians do their main shopping on STT.

I always bring coffee and enough filters for the week; it's easy to pack and you won't have to buy a whole package of filters for just a few days.