One way to get to the falls is by a scenic 1-hour bus ride from Shuzenji, which is 35 minutes from Mishima Station 三島駅 that's a 12-minute train ride from Atami (SUICA/PASMO can't be used so you should buy a train ticket from the machine). On the left side of Shuzenji Station's South Exit, take the bus from Bus Stop #4 to "Mizudare" (水垂). It's 1290 yen one way or you can buy the Amagiji Free Pass (天城路フリーパス) that's valid for 2 days of Tokai Bus rides in the area for 1900 yen at the ticket booth next to the bus stop. Basically, there's just 1 bus per hour - you can find the timetable from Tokai Bus' Japanese site (9:55/ 10:40/ 11:35/ 12:20/ 13:00...)
The well-maintained trail of wooden stairs and multiple mini suspension bridges is easy to hike, even on a rainy day - mostly down the stairs if you start from Kamadaru Waterfall towards Oodaru Waterfall. It's also well-signposted in English. The walk along the river with interesting rock formations is just gorgeous. It wasn't busy at all when we went on a Saturday afternoon at the end of August. There are also some vending machines here and there as well as a few restaurants closer to Oodaru Waterfall 大滝, where there're outdoor hot spring pools right by the fall (entrance through Amagisou 天城荘 for 1500 yen or just 500 yen to see the fall - all other falls are free to see).
There's another bus stop for Shuzenji/Kawazu called Oodaru Iriguchi (大滝入口) - the last bus back to Shuzenji is at 5:30 pm (16:46/ 15:26/ 14:36/ 13:56/ 13:11... before that). There are 1 or 2 buses per hour and apparently it's not in operation during the summer holiday so make sure you check.