Let's go for a drive

I've finally decided to take a day off and go for a solo drive.
I haven't had any time due to work, but the weather is amazing, and as a bonus, premium gasoline prices have dropped to the 2,100 won range lol.
It's the perfect time to just drive without a care in the world.
I live in Yongin, and I'm debating whether to head down to Jeolla-do to see the horizon and grab a bowl of sundae-guk in Iksan, or go to Gangneung for some yukgaejang and an iced americano.
I'm looking for somewhere as far as I can go—where should I head?
Please give me some recommendations.