Recently I was asked by a friend to give some recommendations for a trip to Japan to be done independently, as in, not with a tour group. I'll expand on the information I offered, and give some general recommendations on planning a trip to Japan.
The two main entry points to Japan are Tokyo and Osaka (the 2 largest cities), Narita, Tokyo's main international airport is an hour away in the countryside, Kansai, Osaka's international airport is an artificial island off the coast and is much closer to the city. Unless you really want to see Tokyo, it's possible to base yourself in Osaka or one of the cities nearby such as Kyoto or Kobe and just travel in that particular part of Japan without going up to Tokyo. (I lived in Japan for a year before I even went to Tokyo!)
Buy the JR Railpass!!! This is the best advice I can give, well worth the money, it can be used for JR local trains as well the Shinkansen (the bullet train) Validate it at the airport when you arrive and you can use it on the trains into the city.
Suburban train station in Tokyo on the Yamanote line, the circular line that goes around central Tokyo. Also the busiest line, part of an authentic Japanese experience is to catch these trains during rush hour!! You will never think public transport is crowded in your hometown after being crammed like sardines in one of these trains!
If you base yourself in Tokyo, besides the Tokyo attractions, it's also possible to do day trips to Hakone, to see Mt Fuji in the distance. Kawagoe, just north of Tokyo is called 'Little Edo' as it has an historic part that survived World War II. Kamakura, with the large Buddha and it has a beach so popular with day-trippers from Tokyo as well.
Tokyo itself, I suggest staying in the Shinjuku area, huge transport hub, close to the Harajuku area which is popular, Shibuya with its 5way crossing which I love to watch! Go up to the Starbucks across the road and it has large windows that face onto the crossing, great people watching, best though on a weekend when it's crowded!
Asakusa, has the large lantern Kaminarimon over the gate to the temple, walk down past various stalls, great for buying your Japanese souvenirs.
There's a great park Shinjuku gyoen with the most fabulous displays of cherry blossoms if you're there during cherry blossom season. (early to mid April depending on the weather)
Taking the train south, sit on the righthandside, as on a clear day you get a really good view of Mt Fuji.
This is one of my pictures from last year.
Osaka, Kyoto and Kobe are all very close to one another, most people choose to stay in Kyoto due to its historic past. But modern Kyoto is very spread out, (Osaka even more so) so I suggest Kobe, much cheaper, smaller city, easy to walk around, only 20 minutes by local fast train to Osaka, 40 minutes to Kyoto. (Shinkansen speeds are faster but the stations aren't as convenient)
Niji Castle complex with the Ninomaru Palace, it has the 'nightingale floors' the carpenters who constructed the floors made the so that they would squeak (nightingale noise) when stepped on. A protection against ninja attacks!
The Golden Pavilion, it's a bus ride from Kyoto station, but worth seeing, very popular with local tourists be prepared for crowds!
I took some friends to Japan and they wanted to be dressed as Geisha so I found a photographic studio not far from Kyoto station, where they had the makeup applied, dressed and posed in various traditional poses. It was great fun so can recommend it.
The Gion district is the Geisha area, if you are there in the afternoon it's possible to see Geisha and the young trainees the Maiko walking around.
Hiroshima (about an hour from Kobe)
Peace Park is a must.
Hiroshima can be done as a day trip from the Kansai area (Osaka, Kobe, Kyoto). Morning at Peace Park, then afternoon at Miyajima island, with the large tori (temple gates) that look as though they are floating in the water during high tide. Deer wander freely around the island, so there are no rubbish bins! Carry your rubbish away with you.
Other day trips if based in Kansai are to Himeji to see the castle, I tell people not to bother with Osaka castle or Hiroshima castle as they are concrete reproductions produced in the 1960s, the originals were destroyed in World War II. But the Himeji one is original from the 13th century and well worth seeing.
Okayama has the second best garden in Japan, the first best, Kenrokuen, is on the Japan Sea side of Japan. Korakuen in Okayama is well worth seeing for garden lovers, especially to appreciate a beautiful Japanese garden.
Kurashiki, beautiful small canal town, with a lovely historic centre.
Nara is the ancient capital, before Kyoto, it's a short train trip from Osaka. I prefer Nara to Kyoto as it's much smaller, easier to walk around, it has the Todaiji Temple with the largest bronze statue of Buddha, the park around the temple has tame deer that you can feed with special deer crackers you buy.
For a seven day trip to Japan, this itinerary will get you around to all the main sights and you'll only have to plan accomodation in 2 cities.
If you want to spend longer, a trip to Takayama is worthwhile, the train trip through the Japan alps, while slow (it's not the Shinkansen, but a local train from Nagoya) it is scenic.
Nagasaki is also a nice city to visit, again the Shinkansen doesn't go all the way there so need to change trains.
The northern island of Hokkaido has great skiing and Okinawa is interesting, it's subtropical and Japan's version of Hawaii or the Gold Coast or Costa Brava (depending where you're from!) Palm trees and resorts for summer holiday makers.
Japan isn't that difficult for independent travellers, while some English is spoken in the larger cities, all the signs that are written in the Roman alphabet are in English. You can ask for an English menu or look for a restaurant or cafe with plastic food in the window and point to what you want!
The towns and cities are clean and safe to explore, even to wander around late at night.
Accomodation wise, there are the standard western big hotel chains, the smaller and cheaper business hotels, the traditional Ryokan. Many visitors to Japan try and spend a night or 2 in a Ryokan and they're lovely but also somewhat pricey, having Japanese friends meant that I did the cheaper version the Minshuku (Japanese B&B) There are also hostels, and capsule hotels for very cheap stays!