Thrifty traveling can be tedious
Welcome to the RTA forums. :)
How much money you spend depends on how determined you (all) are in keeping costs to the extreme bare minimum. But be wary, sometimes you can worry so much about trying to save money at every turn that you end up not enjoying why you took a trip in the first place.
My folks and I have been road tripping for several years now, and over time have learned how to become pretty frugal with our expenditures. We first started out at about $360/day ($120/day x 3 people) but we've gotten it down to a science and we now average about $270/day ($90/day x 3). This includes vehicle rental, gas, lodging, all meals, souvenirs, entry fees, and other miscellaneous items. We take advantage of special deals, coupons, and park passes to help maximize our trip experience.
As far as food, I suppose you could get by on $6 per person per day, if you consistently buy groceries. But it sounds like you'd have to do some cooking, which takes a decent amount of time, time you could be spending on the road, and you'll need a place to cook, not to mention all the plastic ware and paper plates for each meal, and of course clean-up. And you want to do that 2-3 times a day for 20 days straight? Hmm... doesn't sound all that enticing, but hey that's just me.
Our routine was to get a cheap breakfast (usually McD's), then snack on random things during the day (fruit bars, chips, pretzels, crackers, trail mix, beef jerky) and then find some kind of hole-in-the-wall place for a $6-8 meal in the evening. It usually amounted to $12/person per day. Not too bad, but probably more than you want to spend. You can make it cheaper by cooking, but not sure if it's worth it, for the reasons I listed previously.
I don't know where in the world you're getting your $440 lodging figure from, unless you plan to stay in hostels or camp every single night. Between 6 people that just sounds unrealistic to me. I figured you'd want to sleep in a nice comfy bed at least once in a while. But hey I've only camped twice so I really don't know the true costs in that arena. I do know you have to pay for a camping spot in some places so if you want a real roughing-it experience and just camp all the time, map out all your potential camping spots on the route. Also make sure it's some place that won't be full up and put you out of luck, which can easily happen during the summer. Reservations may be wise, but that puts you on a timed schedule for the day, which you may or may not want.
You've probably overshot for gas, since it's not really anywhere close to $3/gallon. But I wouldn't adjust that budget. Who knows in this economy, it may very well again come close to that figure by the time summer rolls around. If it stays around $2/gallon, move some of that budget over to the lodging or food arena.
I take it all 6 of you are in one vehicle? That doesn't leave much room for packing, especially if you want to take enough camping gear for everyone (unless you're putting it on top). Of course, I take everything plus the kitchen sink when I travel, so you may be more simplified to your necessities than me.
Most of my travels have been in the western half of the U.S. so I can't really tell you what to expect on the east side. Someone else will have to take that torch in this forum.
But my final say, I think your overall budget is probably too low for 6 people. I'm going to guess between $3000-4000 for everything is more reasonable, however still too low for my taste. Between 6 people that's $500-650 a person, which for 20 days is pretty outstanding. I don't think I could do that myself, but since lodging is the most expensive item on our trip ticket, your methods may be more efficiently budgeted than ours.
Good luck!
