If you want to see some countryside, Nikko is a good day trip, provided that you leave early in the morning (on the Tobu Line from Tobu Asakusa Station).
If you're coming from Korea, jet lag won't be a problem, so while I wouldn't advise an out-of-town trip for anyone on a short visit who had to cross oceans or continents to get there, but if you've given Tokyo a once-over and want to get out of town, Nikko is a good bet.
If you don't want to spend so much time traveling to your non-Tokyo adventure, you could always take the train to Kamakura, home of the Great Buddha of calendar picture fame. Trains leave a couple of times an hour from Tokyo Station, and you can take in the historic and artistic atmosphere of a smaller town and maybe even a ride along the coast on an old-style choo-choo to the island of Enoshima. On weekends, students who want to practice their English congregate at the station exit to act as volunteer guides. All they ask is that you pay for their admission fees and lunch.
When I lived in Tokyo many years ago, Isetan Department Store in Shinjuku was supposed to be the place to go for Western-sized clothes, but I don't know if that is still true. I've noticed that many of the department stores now have larger sized clothes in women's wear, but I don't know if the same is true for men's wear. Since Tokyo is much more international than it used to be, department stores may have learned to accommodate the growing population of foreigners. All the major department stores have information desks, so you can ask there.
For less formal wear, T-shirts and the like, Uniqlo has saved me numerous times when I suddenly needed longer or shorter sleeves than anticipated, due to changes in the weather.