Leaving Gora at 09:05 by train and changing at Hakone Yumoto, Odawara and Ofuna, you will arrive in Kamakura 11:06. Leave your duffle bags at the station and explore the town. In the afternoon leave Kamakura by Shonan Shinjuku Line at 16:39, change at Totsuka and Shinagawa and arrive at Yurakucho at 17:34. There are trains back to Tokyo/Yurakucho every 10 mins or less with up to two changes and this is just an example.

Without knowing exactly what you want to see in Kamakura it's difficult to comment but in addition to buses, Enoden and walking, you can use taxis or one of these. Much less hassle than driving.