It's a very charming and retro resort town, which some will consider outdated, something like Japan's version of Acapulco. But I actually like this old-fashioned scene, as this nostalgia is disappearing so quickly in Tokyo and being replaced by the a la mode places to live or be seen, such as the Roppongi and/or Omote Sando Hills, and the Mid-towns, and the like.
Even Atami's 1960's charm may not last: quite a few of Atami's long-defunct hotels are now giving way to new modern residential tower blocks (most of which will feature a special tap for the bathtub for hot spring "onsen" mineral water, which is Atami's specialty after all), and given Japan's current ageing crisis which is forecasted to only increase for at least the next generation, many state-of-the-art pensioner nursing homes are increasing as well.
The Atami Castle is located at the top of a peninsula cape which overlooks the city. It is less an authentic castle (as it was reconstructed in the 1950's, and the interior features nothing authentic), and more of a tourist museum.
Access by public transport is by the Tourist "Yu-Yu" Bus, or by the Atami ropeway.
Exhibitions located within or nearby this castle are the:
Photography studio for playing dress-up in period costumes (yes, very tourist trappy, but children will love this...),
Samurai Warrior Culture Artifacts,
other traditional painting exhibition,
Ukiyoe Woodblock Shunga Gallery (minors not permitted and sorry but I'm too shy to upload the details so search keywords for yourself),
and the much gaudier Atami Secret Treasures Museum (cheers, o00o!) which is located about one minute downhill walk from this castle.
Opened since 1886, many of the plum trees are about this old. From December-January (depending on weather sometimes in early February), the fragrant flowers are in peak bloom, drawing many visitors here. Atami is well-known in Japan for these gardens.
Off season, it is still a nice place to visit as there are some other flower or autumn foliage which are lovely to view. These were photographed in early October, and literally nobody else except one garden maintenance staff was here on this day during this time. (I've visited during peak season ages ago, and was surprised at the difference in crowds.)
Within these gardens, you may visit the Nakayama Shinpei Memorial Building which is a nice building of traditional architecture (Nakamura was an early 20th century popular music composer), as well as the Korean Gardens at the far end top of the hill.
The "Kiunkaku" was a luxury lodge and garden with Japanese and Western architecture constructed in 1919, and frequented by the literati and dignitairies of the day.
Though it is no longer operating as lodging, it is now a popular as a film location spot for period dramas, and open to the public as an open walk through museum, having been designated a cultural property in 2000.
Accessible by 20 min. walk from JR station, or else just outside by the "Yu-yu" tourist bus Kiunkaku Stop.