Atami means "hot ocean". The town has been a popular hot spring resort since the 8th century and is ranked as one of Japan's Three Great Hot Springs (三大温泉 Sandaionsen). These days the coastline is heavily developed and covered in "identikit" concrete hotels, but in summer the sandy beach is popular.
You can reach Atami from one of Tokyo's two airports. From Narita Airport, take the Narita Express train to Shinagawa, then transfer to either a Shinkansen Kodama train or a Tokaido Line local train. It is 2 hours via shinkansen connection (¥7100) and 3 hours via local connection (¥4900).
From Haneda Airport, take a Keihin Kyuko line train to Shinagawa (¥400) for connection to the Shinkansen (1 1/4 hours, ¥4500 total). Alternatively you can take the Keikyu Line from Haneda to Yokohama via Keikyu-Kamata station (¥470) and change at Yokohama for the local JR Tokaido line (2 hours, ¥1750 total).
Atami is on the Tokaido Shinkansen main line, just 50 minutes from Tokyo (¥3570 for an unreserved seat). All Kodama trains stop at Atami, and a select number of Hikari stop there as well.
Kodama trains make the run to Atami from Shizuoka in 40 minutes (¥2960 unreserved seat) and Hamamatsu in 70 minutes (¥4930 unreserved seat).
Atami is also a stop on the regular Tokaido Line which runs from Tokyo (2 hours to Atami, ¥1890), Shizuoka (80 minutes, ¥1280) and Hamamatsu (2 3/4 hours, ¥2520).
With the exception of the Keihin Kyuko line, all train rides listed above are free with the Japan Rail Pass.
Atami's city center is fairly compact, but buses connect the train station to the MOA Museum of Art via a veritable hillside of ume trees (bus no.4, blossoms in March) and several other points of interest.
There is an Y800 tourist bus that links the main attractions including the Atami Castle. It's called the Yu-Yu bus.
The train station Tourist Information seemed to be conveniently out of English information of any description. There is however a great Tourist Info on the sea front, between the main Atami Sun Beach and the Marine Spa Atami.
There are two car hire companies directly across from the Train station: Toyota Rent-a-car 0557-81-0100. Nippon Rent-a-car 0557-82-4588 (both Japanese only).
Don't be fooled into thinking that the 'Hot Springs/Spas' on the town map are onsen baths; they are literally locations where the hot volcanic water pumps up from the ground. Some even have geysers! There is however a free foot-bath directly outside the train station that runs up until the evening. A conveniently placed vending machine sells towels lest you forgot yours.
However, this area does have several excellent onsen open to the public for a small entrance fee.
Atami is a popular day or weekend trip from Tokyo for scuba diving, largely due to its proximity to the city (40 minutes by shinkansen). Sites feature some spectacular soft corals and sea life including nudibranchs, moray eels, and octopus. Atami also has one of the only divable wrecks in mainland Japan. Visibility can be poor during certain times of year, but it peaks toward the end of the summer/early fall.