At the head of the Izu Peninsula, Mishima isn't that well known, but is an attractive town with a relaxing atmosphere and plenty to see and do. It's perfectly possible to see the town as a day-trip from Tokyo, to combine it with a trip to Hakone, or to stay a night or two and explore the peninsula and other nearby sights.
What to see and do
The main attraction is the Clematis Garden, a cluster of museums, shops and restaurants in the north of the town; arrive early enough and you can get the first free shuttle bus from the station. For more art there's the Ooka Makoto Kotoba Museum, Sanshin Zen Gallery and the Sano Art Museum, which has an attractive traditional garden next to it.
Another draw is the impressive Mishima Taisha, an important Shinto shrine with attractive grounds, and just across the road is a stylish little shopping center called Taisha no Mori. There are also plenty of charming small temples dotted around the town, among them Rinko-ji and neighbouring pair Renkei-ji and Jorin-ji. And if you can go a little out of the way, a twenty-minute walk from neighbouring Kannami station is the small but interesting Buddha Statues Museum.
If you'd like to break up the sights with some greenery, then right next to the station there's Rakujyu-en, a large park that also has a miniature zoo, a beautiful old Japanese residence, and lots of rides for kids. Further away there's Kakita River Park, a more natural space marking the source of a local river, which you might combine with a trip to Sun to Moon, a large shopping mall. Finally, a bus ride away is Yamanaka Castle Park, the site of an ancient hill fort that also has a nice view of Mount Fuji.
Where to eat
While Mishima is renowned for its eel dishes, there are a whole host of different places to eat. For cheap'n'cheerful, near the station there's Naoyoshi, an old-school Japanese izakaya (dining bar), steakhouse Shioya, and Jeet Curry, a cosy little Indian restaurant. If you go to Sun to Moon, there's a food court and a handful of cafes and restaurants in the mall, or Peking Noodles nearby. Back in the centre, Jun is a long-established place to get hearty comfort food, Mishima Terrace and (if their terrace is open) Pasteria Chichukai are nice places to eat Italian food outdoors, while K's Diner and Rin Nouvelle Japonaise offer classy but still very affordable dining.
How to get there
Mishima is on the Tokaido Shinkansen (bullet train) line, though only the slower Kodama (and occasional Hikari) trains stop there: there are two departures an hour from Tokyo and Shinagawa stations, and the journey takes about 50 minutes. If you're on a budget and/or not in a hurry, then the regular train will get you there in about two hours, though you'll probably have to change at least once, possibly at the seaside resort of Atami. If you're driving from Tokyo, it looks like you can do it in around two hours via the Tomei Expressway, while if you're coming from Hakone, there are regular direct buses to Mishima station.