Looking to save some yen and at the same time get a great view of Tokyo. Then check out Tokyo Metropolitan Government Building Observation Decks.
The tallest building in Shinjuku, offers great views of Tokyo, and all the way to Mt. Fuji on a clear day, from the 45th-floor observatory.
It's really easy to get to from Shinjuku Station, just remember to look up for the signs that say "This way to Tokyo Metropolitan Government Building". Just keep looking out for the signs (there are many) and you will be OK.
Helpful Hint: If you get to the station mid-morning of mid-afternoon (weekdays) you can miss the masses; still busy but not as bad as peak hour - please avoid early morning and evening because you don't want to be there when the perfect storm of salary men/woman hit the station. They be in a hurry to get home. Public holidays are the best, the business guys disappear, tourist only, easy as.