I really have to agree with Lifey,

There is a difference between being frugal and watching your budget on a trip, and trying to do a trip so cheap that you can't actually enjoy it.

100 miles is 4 or 5 gallons of gas in an average car, so you're talking a difference of less than $20. Now, I'm not going to be driving down the road tossing $20 bills out the window, but if $20 is the difference between you going someplace or not going there, then I really have to wonder if you have nearly enough money to make this trip happen.

You should be making the assumption that you're going to go significantly more miles than just point to point distances anyway, factoring things like driving to store, within parks, etc. That usually will add about 20% to your total miles. You also simply need to have money in your budget to deal with the unexpected, which could be a mechanical repair or a million other things that might come up.

Even doing this trip very frugally, the size and scope of this trip is going to put the bare minimum costs at $2,000-3,000, and if you are worried about something costing an extra $20, I wonder if you've really given yourself a realistic budget.