Kamakura
An easy day trip from Tokyo, Kamakura is less than an hour from Shibuya Station by commuter train. Kamakura has two hiking trails and a beach, as it's on the Pacific coast, but the big draw here is the Daibutsu — the big bronze Buddha statue on the grounds of the Kotokuin Temple. Cast in 1252, it's more than 13 meters, or 43 feet high, making it the second-largest in Japan (next to the one in Nara, the ancient capital south of Kyoto) and the largest one that sits outdoors — the wooden temple structure that once housed having been destroyed in a tsunami about 500 years ago. The temple (open daily from 7 a.m. to 6 p.m., or 5:30 p.m. in winter) is near the Hase Station on the local Enoden line; take a JR train from Tokyo to Kamakura Station and transfer, or get off at Kita-Kamakura and take the hiking trail.
Also worth visiting: Hase-dera, a temple known for its many Jizo statues. There are thousands of them clustered around, on ledges and along stone paths and stairways. The Jizo, a Japanese form of bodhisattva, is believed to be the guardian of children and is usually depicted as a Buddhist monk, so we're talking herds of little bald men, some wearing crocheted hats and capes to help keep them warm. Hase-dera is open daily from 8 a.m. to 5 p.m. (4:30 p.m. in winter).
Odaiba
Take the 20-minute sea bus ($4) from Hinode ferry terminal or the monorail from Shimbashi (20 minutes, $3) out to this manmade island in Tokyo Bay for a walk along the beach and a view of the Rainbow Bridge. There's also a big shopping mall, enormous ferris wheel, and Sega's Joypolis, a massive indoor amusement park. Sony's ExploraScience Museum here is great if you're traveling with kids; even adults will be entertained by the museum's interactive exhibits and virtual reality games. Admission is $5 for adults, and $3 for children ages 3 to 15. (Note: the museum is temporarily closed for renovations, but will reopen in June 2009.)
Close by is Oedo-Onsen Monogatari, a spa retreat where you can take a restorative dip in one of the many onsen, or hot-spring baths (they are not private, but men and women are segregated). Lounge around the garden in your borrowed yukata robe, soak your feet in the shallow wading pool and massage your soles against the stones along the bottom — or have them exfoliated by "Doctor Fish," the freshwater carp that will nibble away at your flaky skin until you're smooth from heel to toe. (It's actually a delightful experience, and I'm as ticklish as they come.)
In the spa's bathing rooms, you're not permitted to wear your robe, or a swimsuit for that matter, so you'll have to check your modesty at the door. You are allowed to carry a "humility towel," a small swatch you can strategically drape against yourself as you walk about the decks and then fold and place on the top of your head while you're in the water. It might feel awkward at first, baring all in front of strangers and your travel pals, but in Japanese culture it's perfectly, well, natural. Note: no tattoos allowed (skin art is still considered the mark of a criminal here in Japan, even though more and more young people are getting inked). If your tats are small enough, cover them with Band-Aids. Oedo-Onsen Monogatari is open 11 a.m. to 9 a.m.; admission is about $30 for adults (some spa treatments cost extra), and $16 for children ages 4 to 11.
Hakone
Hakone is known for its mountain trails, scenic boat and cable car rides, onsen (hot-spring baths) and art museums, including the fantastic Open-Air Museum, an expansive sculpture garden featuring works by Rodin, Miró, and Henry Moore, plus a Picasso Pavilion. It also has killer climbing ropes for kids in a separate playroom called the Castle of Nets. Try to hit the museum early (it's open 9 a.m. to 5 p.m.), to leave time for this next leg: From Gora station, take the $4 funicular to the Sounzan stop (a 10-minute trip), then get on the Hakone Ropeway, a 2.5-mile (4-km) aerial tram that takes you over mountainous terrain and on to Lake Ashi, offering splendid views of nearby Mt. Fuji along the way. At about the midpoint is Owakudani, an area known as the Great Boiling Valley. Stop off there for a hike up the side of a volcano, where you'll see — and smell — the geothermal gases escaping from fissures in the rock. As a snack you can buy eggs that have been boiled in the hot springs below, turning the shells black. It is said that consuming one of these eggs will extend your life by seven years. Either way, they're tasty.
Hakone is a three-hour journey or less from Tokyo's Shinjuku Station on the Odakyu line. To get to the open-air museum from the Odawara or Hakone-Yumoto station in Hakone, take the switchback train to the Chokoku-no-Mori station and it's a few minutes walk from there.
Kichijoji and Studio Ghibli Museum
Kichijoji is a lovely little suburb west of Tokyo, less than 20 minutes on the express train from Shibuya station. Get off at Kichijoji station and head south to Nanaibashi Street, lined with shops and cafes. At the end of that road, before the big steps, you'll see Iseya Sohonten, a big smoky yakitori restaurant and Kichijoji institution, on your right. If you don't want to dine in, you can order skewers of grilled meat and corn on the cob from the take-away counter and continue on into Inokashira Park. There's a pretty lake lined with cherry and maple trees, so you get the blossoms in the spring and autumn leaves in the fall. Rent a paddle boat in the shape of a swan, or follow the lovely trails that lead through the woods, past a pretty red Benzaiten shrine and an interesting Thai restaurant called Pepa Cafe Forest.
In the West Garden of Inokashira Park, past the lawn tennis courts, is the Studio Ghibli museum, where you can admire the work of Hayao Miyazaki, the Japanese anime master behind Spirited Away, Princess Mononoke, My Neighbor Totoro and other films. There's a big furry cat bus to play in, a giant robot on the roof, artist sketches and cels and a trippy zoetrope. The museum is geared toward kids, but Miyazaki fans of any age will enjoy it. The theater shows a short film that you can't see anywhere else.
Tickets for the Ghibli museum (open daily from 10 a.m. to 6 p.m.), which cost $10 for adults and $7 or less for kids, must be purchased in advance, and they often sell out on weekends. Unfortunately, you can not buy tickets online. Some travel agents in major U.S. cities can sell them to you, or you can try your luck at a ticket kiosk in any Lawson's convenience store in Tokyo. The menus are all in Japanese so ask a store clerk for help. Click here for more information on the ticket sales system.