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I think your budget for a rental car may be one of the toughest things you have to deal with. While the regular rate for a month long car rental will likely be around $700-1000, depending upon the model and company, you're also going to be dealing with a young driver rates. There is typically a $20-25 dollar fee per day for drivers aged 21-24.. Assuming you want to have more than one driver, you could also be looking at another extra fee there too. When you factor in those charges, plus other taxes that are typically placed on car rentals, I suspect you'll be looking at spending around $2000 for your car rental.

A month will be enough time to do a lap around the US, but as far as a best bang-for-your-buck route, that's going to really depend upon what you want to see. I'd start simply working with your friends and create a list of what places you'd really like to go, then you can work to build a route around them, or decide what might be just to far away to really work into this trip.