I know this is a difficult question to be answered, I'd have problems and I'd have to consider many things to answer this question about my country, so I'll try to be as specific as possible.
I'm going to Japan for 10 days in beginning of October with a friend, and I'm not sure where to go.
I’d like to try to mix some big city (probably Tokyo once we’d arrive there) and some other(s) nice place(s) / city(ies).
I’ve read nice things about some places like Hokkaido, Nagasaki, Atami, Kyoto. Not sure if those cities are pretty much similar to Tokyo in a way. I’d like to go to some castles, small typical beautiful cities.
Where would you go?
Thanks a lot for your comments, feel free to ask some more information you find useful to answer this question ok?
Tokyo and Kyoto are each worth several days, especially if you do a day trip from each. For example from Kyoto you can easily reach Nara for a day trip..
Other places of interest might be Hakone (2 hours from Tokyo where you can experience hot springs and, if lucky see Mt Fuji), stay at a Buddhist temple on Mt Koja or see the Torii in the water at Miyijima and visit Hiroshima. Only the latter are outside the Tokyo or Osaka area.
Kyoto is very different than Tokyo, a bit slower paced and full of wonderful temples and gardens.Himeji Castle is not far from the Osaka area, although there are castles in Tokyo area and in Kyoto.
I hope you have a wonderful trip!
For a ten day trip I would not go to Hokkaido unless you have a strong interest. It's isolated from all the other places, so if you go there, that will pretty much be it.
A typical tour would be Tokyo, Kyoto, and Hiroshima with some excursions (ex: Visiting Nara from Kyoto, Nikko from Tokyo, etc.). For ten days, it works well. Kyoto and Nara will give you a feel for more traditional Japan.
I'd also suggest going to Hikone. Hikone Castle is an original castle, it has a garden, and some buildings from its castle town days. You can go as a daytrip from Kyoto. Himeji Castle is under rennovation, so it's covered by scaffolding (NOT impressive at the moment).
If you don't care about seeing original castles, then you can go to any old place (Osaka, Hiroshima, Nagoya, etc)
Some traditional places around Tokyo are Nikko, Kamakura, and Kawagoe if you'd rather save money and explore the Kanto area, but I think Kyoto as well as Hiroshima are worth the trip.
10-day can only do Hokkaido. Skip it if it is your first time to Japan. Above VTers' suggestions are nice.
I would agree with the people suggesting Tokyo and Kyoto. Both are definitely worth several days.
One additional place to consider might be to head to the holy mountain, Koya-San and visit there. The town is the centre of the Shingon Buddhist sect and doing a temple stay for a night or two and poking around town is really quite interesting. It's about a 2-hour train ride out of Kyoto, so quite doable in your timeframe.
Everyone here has pretty much the same answers, and mine are almost the same too.
I believe Shrimp is talking about Mt. Koya, not Koja. GrumpyDiver has the correct name.
For 10 days, Hokkaido would be a bit tough. Same for Nagasaki. Atami, you can do it but it isn't really worth it. You are better off sticking around Kyoto.
While I think Hiroshima is a good place to visit, I don't know if you have enough time to really enjoy it. You need about 2 days to visit it. From Kyoto, it isn't too bad but getting to Miyajima isn't really easy and you'd only be able to see Itsukushima Shrine. Going up the mountain would be doable but it might be rushed. Depends on how early you leave and how soon late you return to either Hiroshima or Kyoto.
If you go to Kyoto and Nara, I would skip going to Kamakura and Hakone. I would still consider Nikko as it is very different from things you will see in both Kyoto and Nara.
If you want to see castles, Hikone, as mentioned, is your best bet. Himeji is currently undergoing renovations but you can get into a special tour where you can see the roof up close as they conduct renovations. Not too sure how to get into the tour though, but it isn't really worth it unless you are into architecture and construction.
For 10 days, I would split it evenly between Kyoto and Tokyo. Tokyo for the modern city life and shopping, and Kyoto for history and temples. Nara would also take a full day. If you head to Hiroshima, as I said earlier, take a couple days, 3 are best, from your schedule. Travelling will take a lot of time if you take the trains but not a full day. You still get half a day in each area.
Where to go in 10 days depends on your interest. If you love nature hikes Hokkaido is worth staying for a few days but you may have to define what area because Hokkaido is so large. If you love onsens 10 days are not even enough because there are so many great onsens. If you love Japanese gardens visit both Kyoto and Tokyo. So defining what you want to do in Japan is the very start of great tour plan.
We spent 10 days in Japan and we could visit Tokyo, Osaka, Kyoto, Nara and Hiroshima. We got our base in Tokyo first and then moved to Kyoto and later to Hiroshima. Osaka and Nara were day trips. You can read lots of tips about our holiday in Japan in my homepage. Just click on the links where I indicate Tokyo, Kyoto, etc. Enjoy Japan :)
Day 1 - Land at Narita Airport and take the train to Tokyo. Rest and recover from your flight.
Day 2 - Visit Nikko and explore its complex of temples and shrines at Toshogu.
Transportation: at Tokyo train station, take the JR Shinkansen on the Yamabiko Line to Utsunomiya train station. At this station, change to the Nikko Line and go to Nikko train station.
Day 3 & 4 - Visit Hakone in Japan's famous Fuji-Hakone-Izu National Park.
Transportation: Return to Tokyo train station and take the JR Shinkansen (Bullet Train) to Odawara train station. At Odawara, you can buy the Hakone Free Pass (3 days for 4,130 yen) which gives you access to Odakyu railways, cable cars, buses, and boats. Hakone
Day 5 & 6 - Visit TAKAYAMA, a culturally rich and historic scenic mountain town.
Also, Shirakawago which contains thatched-roofed houses and is one of the most picturesque villages in Japan.
Transportation: take the JR Shinkansen train to Nagoya, and then at Nagoya take the Express train to Takayama.
From Takayama, it is a 2 hour bus ride to Ogimachi with a bus change in Makido. (If you have a JR Rail Pass, you can use it between Makido and Ogimachi and only buy the ticket between Takayama and Makido)
Day 7, 8, 9 - Visit KYOTO, the ancient capital of Japan. This city contains hundreds and hundreds of temples, shrines, gardens, as well as the old Imperial Palace.
time permitting, a one day trip to Nara is also recommended.
Transportation: take the Express train from Takayama to Nagoya, and change to the JR Shinkansen at Nagoya and take it to JR Kyoto train station.
Day 10- Take the JR Shinkansen back to Tokyo train station and take the Express train to Narita Airport.