Marble Lounge (Inside Hilton Tokyo Hotel)
Let's get this one out of the way first. The Hilton's Marble Lounge is one of the best in the area, especially if you love sweets. They have an impressive dessert buffet developed by world-class patissier (sweets buffet is served between 14:30 and 17:30). They have different buffets for breakfast, lunch and dinner time (sweets are of course available for the lunch and dinner buffets). The dinner buffet's signature dishes are crab legs and teppanyaki beef. The menu changes with the season, so you get some of the western and Japanese foods made from top quality seasonal ingredients. If you just feel like not going out of the Hotel, then don't feel as if you're missing out, because the Marble Lounge is legitimately an excellent restaurant, and the buffet courses are actually reasonably priced for the quality.
Itamaegokoro Kiku-Ura 板前心 菊うら
We highly recommend this Japanese restaurant of kappo cuisine! Kappo is a traditional style of cuisine that serves many small refined dishes in a course meal. It includes sushi and sashimi as well as cooked and boiled fish. This is a quintessential Japanese cuisine you will love to discover. What's nice about his place is that for lunch, you can get set meals for less than ¥2,000 (some kappo courses are also available for about ¥4,000) and for dinner, you can have the much more elaborate kappo courses that are about ¥7,000.
This restaurant near the Seibu Shinjuku station, at about a 10-minute walk from the Hilton Hotel.
This might be a bit surprising but Tokyo has some really outstanding Indian restaurants, and among them, Cochin Nivas is one of the best! What's more, this place is really reasonably priced (dinner: ￥2,000～￥2,999, lunch: ￥800～￥1,999)! The place specializes in Southern Indian cuisine. They use a good amount of fine spices which give the dishes a more complex taste than the general Indian cuisine in Japan. Try their lemon rice! It's said to be one of the best things on the menu. This small and secluded restaurant is always packed because of it's popularity with the locals.
Located at a 7-minute walk from the Hilton Hotel.
Darumaya だるまや 西新宿店
Darumaya is an iconic restaurant serving what many consider to be the best Hokkaido-style Japanese BBQ called the Jingisukan (comes from "Genghis Khan"). A Jingisukan is somewhat similar to a yakiniku meal, but the made type of meat is lamb, which is quite unusual in Japan. Also, the food is grilled on a skillet resembling a Mongolian warrior helmet (hence the name "Genghis Khan"). Darumaya has a really nice, warm atmosphere. If you like meat and barbecuing, you will love this place, guaranteed!
Menya Shou 麺屋 翔 本店
With its hoards of businessmen and students, Shinjuku is a FIERCE battleground for ramen. Menya Shou is one of the best according to many ramen junkies in Tokyo. You can't get a reservation to get in and you often see long queues in front of this joint. So if you plan to go there, try to go outside of the peak lunch or dinner hours. Their number one dish is their shio ramen ("salted ramen") which is made with simple seasoning but a deep-flavoured chicken broth so full of umami that you just get completely addicted to it and keep going back for more! They also have some tsukemen (dipping noodles) that are a different twist to the standard bowl of ramen. They serve the tsukemen noodles without a soup. You dip them in a rich sauce instead.
Hope you'll enjoy discovering some great restaurants around the Hilton Tokyo Hotel! Here's some bonus information below for all of you ramen junkies!