If you look at the map outside the south exit of Mishima Station, you'll see a big patch of green more or less immediately next to the station. This is Rakujyuen, the municipal park, which is much more enjoyable than that title might make it sound; there's attractive landscaping to enjoy, fun facilities for families with kids, and a beautiful old Japanese residence to admire.
About half the park is given over to woods, where a lot of different trees and plants grow in the fertile volcanic soil. The paths wind gently through the trees, and the atmosphere here is very pleasantly relaxing; there are a few handy benches for you to sit and take in the peace, perhaps over a snack or picnic lunch. There are also a number of ponds here, though the largest has dried up owing to the groundwater being diverted for industry; the result is a kind of moonscape, with large volcanic rocks scattered here and there on the ground.
In the middle of the woods is the Rakujyukan, the former villa of an Imperial prince at the time of the Meiji Restoration around the end of the 19th century. It's worth taking the free tours given six times a day (the English leaflet says twice a day, but is out of date); they're given only in Japanese and you're whisked round pretty quickly, but you'll still be able to enjoy the airy wooden interior, and exquisitely beautiful paintings on some of the screen doors and ceilings.
The other part of the park is aimed squarely at families with young kids. The are rides like a merry-go-round and a miniature train for ¥100 a go, and an "animal park" with a selection of cute creatures, among them ponies, alpacas and a colorful lesser panda. There's also a small house of mirrors where you can watch yourself change shape, a parked old steam locomotive for you to climb up into and pretend to drive, and near that there's also the Mishima City Museum of Local History, with briefly diverting exhibits of (presumably local) industrial products and artefacts.
As well as all that there are a couple of shelters and some outdoor tables to rest at, and a cafeteria serving snacks and light meals such as noodles and hot dogs, There's a small entrance charge of ¥300 (¥50 for children from 4-14, free for infants), but with all the different things to enjoy, it's a very pleasant place to walk around and explore, and there's bound to be something for everyone to enjoy.
