While you could certainly do this without any Visa implications - the challenges you will have are around:
- storing your vehicle
- sunk capital cost of vehicle
- cost of Fuel & Vehicle maintenance
- Your time
In short, there is an economic reason why plane travel continues to grow. It does make economic sense.
I have not looked into it - but possibly if there is a train that goes between your cities that would be a viable alternative to the idea of using a car the way you describe? And if you do your comparative sums carefully - you may be able to create a positive arbitrage.