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.