There are three ways to get to Atami from Tokyo area. The easiest way is to take Shinkansen Kodama express from Tokyo to Atami. Only Kodama Express stops at Atami but it is the quickest way to get there.
Another way is to take Odoriko Express from Shinjuku Station. It is slower than Shinkansen and the train cost may take as much as that of Shinkansen Kodama Express. But the train is tailored for upscale tourists and if you want to enjoy the train ride this must be it.
The cheapest way to get there is to take Odakyu Express to Odawara and change trains to Tokai Line bound for Atami, Ito, Numazu, Izukyu Shimoda. When you take that route you need to buy a ticket to Atami(400 yen) and pass the barrier to enter Tokaido Line. But the total cost is 850 yen for Odakyu Express and 400 yen for Tokaido Line and totaling 1,250 yen. So if you can take the early train it is worth a try.
Hatsushima Island is the small island off the coast of Atami. It is connected by 25-minute ferry ride from Atami Port. It has four services a day. There are two type of vessels the larger one is Isle de Vacance III (293 tons) and the smaller one is Isle de Vacance II (184 tons).
This is a handy bus route where you purchase a day pass, and ride at will. You'll receive an illustrated map with timetable. There are two loops: the "Nishikigaura/Baien (Plum Garden)" which is the main Atami city loop, and the "MOA Museum of Art/Mt. Izu Shrine" route. All 33 stops in the combined two loops are at tourist points of interest.
The bus timetable from JR Atami Station operates from 9/10 am generally once every 45 mins. with a missed run during the lunch hour. The bus routes and city points of interest are explained by local senior-aged volunteer guides.
Atami is on the main Shinkansen line, although only the Kodama (the slowest of the services, stopping at all stations) stops there.
From Tokyo the most comfortable (and expensive way) to get there is the Odorikko express.
It is slower than the shinkansen, as it doesn't use the shinkansen tracks at all, but is more comfortable, and stops at Atami on route to Shimoda on the Izu peninsula.
The windows are much larger than on your average train, meaning you get a much better view as you travel along.