Food can definitely be cheap in the States. Eating out is cheap compared to here in NZ anyway! You'll love summer camp by the way, I've worked at 2 different camps before Vegas is a cool place to visit, and the accommodation is cheap if you avoid the themed hotels - we got very decent motel rooms at a place just off the Strip for $35/night. Other personal favourites have been Miami, Monument Valley, Yellowstone, Mesa Verde, Telluride....the list goes on lol. You'll have an awesome trip anyway
There are places like Waffle House who have meals for $3-$5 depending on what you get. You can see those on the side of the road wherever you go.
As far as Buffets go, they usually run between 7-10 pounds (yeah, about $15.00) But you could probably get 2 or 3 meals out of them if you're stealthy. Just ask for a take-out box (or several) and stuff them to the brim. They usually don't care at all.
I Imagine Car Rentals are one of the biggest expenses. I suggest looking into a bus pass, although it's a bit more inconvenient if you have to be somewhere at a certain time.
My knowledge about places-to-go and things-to-do is sort of limited to Florida, though. If you specify what you want to do in Florida, I can give you a few tips!
In glimpsing over the other responses I don't think this was mentioned: Gas (petrol) while cheaper here than many other places will still cost you a good chunk of change. Seeing as you talk about pounds I'm guessing you might be from Great Britain. If you are thinking of driving from Las Vegas to Florida and New York, then think about how much it might take to drive from London to Glasgow about 10 times. Also consider that the U.S. cars have pretty sad fuel efficiency comparatively. Added to that driving from Las Vegas to "Orlando" would take about 25 straight through, and "Orlando" to New York would take about 17 hours straight through. While all very doable, I would consider taking a more direct route from Las Vegas to New York, or flying. If you really want to hit all those places a good combo might be to fly from Vegas to "Orlando" and then rent and car and drive up to New York. Especially, as a lot of that drive from Vegas to "Orlando" would be quite boring. Also if you are looking at rentals, make sure you are looking at one-way rentals. These are a lot harder to find and can add greatly to the expense.
Something else you might want to consider would be Trek America. I haven't done any traveling with them, but have heard a lot of good things from others. This would give you the opportunity to see more places and "drive" across the states without the hassle of rental cars, etc. They have a few different options that start in L.A. and end in New York. One that looks like it could be particularly interesting is the Transcontinental South. It last 35 days, costs about $3000 a person and covers L.A. Vegas, Orlando, the Florida Keys, and much, much more. However, they also have a large variety of other ones, with cross-country ones starting at about 21 days. Not sure if it would be what you are looking for, but it might be something to consider.