We did Masters in 2019 (Saturday tickets even!) It truly is an event like none other - you will have a great time!
We flew BA to Nashville, then picked up a cheap flight on Southwest one way to CLT. Got the car rental there (another CLT perk: there is a plane museum next to the airport where the Miracle on the Hudson A320 is housed), stayed one night, then drove to Columbia which was only a few hours. Got an Air BnB in Columbia and used it as our base - anything near Augusta is gonna be $$$$$ week of the Masters, if you can even find anything at this date. Columbia worked great - it was maybe an hour, hour and a half drive and even after a long day on the course, the return drive wasnt overwhelming or tiring at all as little traffic. Its also a very straightforward drive. Not a bad little town, adorable main street area where we propped up the bar and watched the Sunday finish with other people.
I would say that road conditions in SC are a bit worse than GA, but the drivers were more or less ok. That being said, we are used to American traffic and interstate driving.
For our return we flew from CHS to HOU and then to LHR (after driving up to Charleston and spending a few days in the Georgia Golden Isles). You may need to get creative with exit points and consider taking point to point flights in the US on either AA or Southwest. We flew First on points and IAH was the only airport with availability that wasnt Chicago or NYC.
For Masters tips:
1) Get in and buy swag at the pro shop first thing. Then take it back to your car and return for the golf, so you dont need to drag it all over the place. Parking control is top notch with superb flow, they will have you lined up and parked in no time.
2) No cameras allowed although I think you can maybe take a few photos of the practice green
3) Definitely get one of the green Masters lawn chairs, pick a favorite hole, and park it, maybe stick a business card in the holder on the back or some other form of identifier. No one will take it, its rule of the course
Wander around, try different (cheap) foods and return later in the day when your favorite pair is coming through
4) Augusta National has crowd and line control down to a SCIENCE. The line may look long at the shop/food outlets, but it moves lightening quick. Bring money and don't look at price tags - just accept you are going to drop a wad of cash. At least the food is cheap and the souvenir plastic cups are great.
Im currently pricing up our travel for the PGA in Tulsa in May and car rental prices are insane - be aware that what you may have paid a few years ago will likely have no bearing to reality today. Last year on our trip to Chicago it was about £90 a day for a 4 door car - I wouldnt drive anything smaller than that in the US.