Shinjuku area is a major commercial and administrative centre and it's the busiest railway station in the world! Here is my recommeneded places.
The Tokyo Metropolitan Government Building (the administration centre for the government of Tokyo ) and other high buildings: You can go up to the top and enjoy the Tokyo nice views. It's free.
Isetan Department Store : One of the biggest department store and the annual sales ranks between 6th and 8th always in Japan.
Tokyu Hands in Shinjuku Takashimaya : The biggest Tokyu Hands in Shibuya, but Shinjuku one is located inside of Takashimaya Department building in south exit, you can enjoy department store too and also very big book store Kinokuniya stands next to the building.
Restaurants which you can cook by yourself: There are a huge number of restaurants in Shinuku. I recommend to have "the experience", not only taste.Here is some video who enjoy cooking.
Okonomiyaki,Monjayaki,Okonomiyaki / Konamono Other
Dinner 1,500 JPY
Monday - Friday Dinner: 16:00 - 23:30(L.O.22:45)
Saturday & Sunday & Holiday Lunch・Dinner: 12:00 - 23:30(L.O.22:45)
JR Shinjuku Station East Exit 1-minute walk
Japanese Other,Izakaya (Japanese Style Pub),Fried Skewers (Meat and Vegetables)
Lunch 1,260 JPY Dinner 2,800 JPY
Saturday & Sunday & Holiday Lunch: 11:30 - 15:00(L.O.14:30, Drink L.O. 14:30)
Dinner: 16:00 - 23:00(L.O.22:30, Drink L.O. 22:30)
Shinjuku(Tokyo) JR Shinjuku Station West Exit 2-minute walk
Shabu Shabu : MK restaurant is very very reasonable restaurant you can try Shabu Shabu and sushi etc,.If you want to save costs.
Nabe (Japanese Style Hot Pot),Dim Sum,Sushi / Seafood (Other)
Lunch 1,300 JPY Dinner 2,000 JPY
Monday - Sunday 11:00 - 23:00(L.O.22:30)
Shinjuku(Tokyo) JR Shinjuku Station East Exit, central East Exit 5-minute walk