Even if you don't have a couple hours to spare ... You can find Shinjuku Gyoen National Garden just a couple blocks away from the Shinjukugyoen-Mae metro station. The park is open daily from ...
Golden Gai is about a 10-minute walk from the east exit of Shinjuku Station. Hours of closing vary, but are typically 5 a.m., except for Sundays, when businesses start to shutter around midnight.