GA to Montanna

From Atlanta to Billings, it's 1879 miles according to Mr. Rand McNally (your route may vary!). Their estimate of driving time, each way, is 30 hrs, 15 mins. So three weeks would be plenty of time to see the route and the destination -- Billings is a good starting place to explore Montana.

Costs? Figure out about how many miles you will add above just getting there and back (there is LOTS to see in MT and also along the way), add up the total, divide by your miles per gallon in whatever car you are driving, then multiply the result by the average cost per gallon of gas. Today, AAA says the national average for regular unleaded is about $1.52. That'll get you an estimate of likely fuel costs, but be sure to add an extra amount for a cushion.

Food? If I am eating in cafes/restaurants, I usually figure $20-$25 per person per day -- which is PLENTY, but excludes fancy places. Eat your own food out of an ice chest or a sack, & you can do much better if you're careful about what you buy.

Motels can run from roughly $30 to $100+ -- depends on what you pick. You can find rooms for less than $30, but most people wouldn't want to stay there. Beware of any place that charges for rooms by the hour! Camping can be cheaper.

Those are the major expenses while roadtripping -- add in some spending money and make sure you are prepared for unexpected stuff -- like car repairs, or heaven-forbid, injuries. You need to think about how you'd handle things like that if they occurred.

The most direct route is to go via Nashville and Paducah, then St Louis, generally follow the Missouri River to SD and then across I-90 via the Black Hills and Badlands (or take the Great River Road north from St Louis to MN and then west). You might return a different way to see some different country -- maybe down through Wyoming, Utah, and Colorado and across the Great Plains thru Kansas or Oklahoma (seeing Yellowstone and other great places along the way).