How can I keep ingredients cold while camping?

Here is my camping strategy. If I'm going for more than a few days, here's what I do.

• Start with a good air tight cooler. (Big enough to hold everything perishable). Forget those "gel packs". Definitely don't get a bag of ice from the convenience store. They melt and mess stuff up. Get a 2 litre bottle, rinse it out, fill it with water and freeze it. (Do this a couple days in advance, if possible). The less air in the better. This won't leak and will stay cold a good time as long as you don't open it.
• Take any raw meat that you're NOT planning on eating on the first day and freeze that too. Put the meat and all the frozen stuff at the bottom and to one side. My bottle of ice goes either directly on top of the meat or right beside it. This way, my meat has at least an extra day or two of grace and I don't need to waste extra space with an ice pack.
• Then layer stuff that isn't frozen, but can handle a little freezing on the next layer. Then work your way up, to any produce being on the top layer. Plan for the coldest stuff to be at the bottom and/or near the ice packs. Depending on what's in there, sometimes I put a towel between the frozen stuff and the non frozen stuff to insulate it a bit better. And prevent produce that shouldn't be frozen from freezing.
• Then on each day, I move the frozen meat for the next day meat away from the ice packs and upward to allow it to defrost (making sure, it's sealed, so I don't get any raw meat juice leaking out).
• On the last day, the water in the bottle can be drank, but once you start emptying it, it'll start melting.

Obviously, minimize the time you keep it open if possible. I realize you said you're going camping tomorrow, so freezing a 2 litre bottle might not happen in time. In this case, I'd switch to multiple smaller bottles and failing that those gel packs. I hate bags of ice, as they melt and make a mess. Finding cheese in a pool of water is never fun. The rest of the stuff would still apply. This usually lasts me quite a few days.

Ice chests last way longer than just a few hours. Unless the weather is insanely hot, if you put a reasonable amount of ice in a good ice chest, and don't open it all the time, there'll still be ice in it a couple days later.

We camp at the beach on a regular basis during the warmer months (which is most of the year down here in South Texas!!), and we've found that along with freezing water bottles and proper layering, we can get an extra day or 2 out of our cooler by digging a well in the sand to put the cooler in. The sand acts as a great insulator against the heat, plus the deeper you dig, the cooler the sand gets! Throw some reflectix on the lid of the cooler, and your all set!!

eat the perishable food first. Keep perishable in the shade. Store your food under running water.

I get two coolers one smaller than the other. The smaller one is for cans of soda or a gallon of milk and two liter bottles. Using two litre bottles as ice containers is a good idea as whe the ice melts it will not get all over your food. If you have any bubble wrap stuff it in the top of the cooler to take up dead air space. Bubble wrap or sealed air packages which are common today.

I like to cook up soups, stews, chili, spaghetti sauce, etc. ahead of time, portion into one-meal amounts in freezer bags, and freeze. I use these as the ice in my cooler. I do the same with meats. They don't keep stuff cold as long, but you can get insulated shopping bags now that do keep stuff somewhat cold, especially if you're filling them with frozen food. These are a lot easier to pack into a backpack between campsites. Wrap some blankets and towels around it to add extra insulation.

I also like to bring along as much non- and semi-perishable food as possible. Hard cheeses, dried sausages, dry beans, jerky, pilot bread, dried fruits, nuts, oatmeal, etc.

For fall/winter camping, I like to carry a small, wide-mouth thermos for soup. I heat it up in the morning before breaking camp, pre-heat the thermos with hot water before filling it with soup, and have hot soup for lunch. It's great after a cold morning of hiking.