Shinjuku station is the world busiest transport hub in the world. Accordingly the number restaurant, shop, and leisure in Shinjuku is countless. It is almost impossible to go and experience all in one day!
The reason for this record is because there are 12 railways run by 6 different companies are available. This allows you to easily access pretty much any place in Tokyo. Furthermore, the recent build bus terminal in Shinjuku reinforced the access to major spots in Japan.
To such busy station, you can directly access with train from Araiyakushimae station. Even though it is very close to Shinjuku, the Araiyakushimae area is very quiet and the environment is probably more suitable than Shinjuku. From the house, it only takes 3 minutes by walk to the station. Within such short distance, you can find convenience store, supermarket, and pharmacy. My recommendation is to visit Japanese traditional sweets store. Also, many Ramen restaurants open around the station.
*under 2years free