ONSEN RYOKAN & HOSTEL
Kodama(こだま) Super Express departs twice a hour.
It takes 45 minutes and 3,670JPY.
Local Train from JR Tokyo Station
Local trains often go to Atami from Tokyo station
It takes about 2 hours and 1,940JPY.
First take Hikari Super Express bound for Tokyo(東京), then change trains at Mishima(三島) to Kozama Super Express bound for Tokyo(東京).
It takes about 2.5 hours and 11,340JPY.
Search Transportation: http://www.rome2rio.com/s/Kyoto/Atami
It only takes about 5 minutes and cost roughly 700 yen.
Therefore, I would highly recommend for you to take a taxi, especially, if you have big luggage with you. Please show this sentence below to taxi drivers.
★Walking directions to Khaosan Atami for backpackers: View PDF File
★Driving directions to Khaosan Atami: View PDF File
How to take a bus (PDF)