Harajuku has been known as the capitol of fashion for many years. From the most trendiest fashion right to the most outrageous fashion can be found here. Apart from the main walking street which is known as Takeshita Street, there is also the high end shopping area known as Omotesandō (表参道) Street. Another highlight of this place is the famous Yoyogi Park where on weekends, the best of the best in Japanese fashion can be seen. Among the unique fashion observed here, you see defunct Rockabilly fashion right to the Punk Rock era. From here, the first thing you would notice is the massive crowds surrounding the entire area. A large majority would be mostly teenagers who come here to shop or just hang out. The weekend is the best time to visit Harajuku and you should spend at least half a day there. Go in the late mornings till the late afternoons.
You'll need to set of early so I recommend catching the Odakyu Express Train from Shinjuku to Odawara at 9am (all included with the HFP). From here you can jump on the Hakone Bus to Hakone-Yumoto station followed by the railway to Gora. By now it will be around midday so you might want to have lunch in Gora. If you consider yourself a bit of an adventurous foodie then try the local delicacy of 'black eggs.' Just remember to hold your nose!
If you love hiking, visiting the Miyagase Information Center is one of those times where you wish you knew Japanese. It showcases infinite information about the best hiking destinations in Kanagawa and the surrounding prefectures. Brochures about preparation and safety before the big hike. The Information Center also offers craft activities for all ages using natural materials.