Japan-cities to base in?

I am traveling Japan for 2 months and am hitting a lot of cities. Therefore, if anyone can help by telling me what "base" cities to stay in and what places are reachable from those bases? For example, I would like to visit Kyoto, Nara, Mount Koya, and Himeji. Thus, I have been told I should book a hotel in Kyoto and take side trips to Nara, Koya, and Himeji. In addition, what would be the best route to take to visit all the cities? I have tried my best to figure out the routes and staying accommodations but am having such a difficult time! Any help would be appreciated. Thank you :)

My destinations are:
tokyo
matsumoto
himeji
takayama
kanazawa
nagoya
kyoto
osaka
kobe
nara
mt koya
hiroshima/miyajima
fukuoka
mt fuji
Ise
chichibu
nikko

and possibly if time permits:
matsumoto
kamakura
noboribetsu
hakone
okinawa
shirakawago
hachimantai
magome
yokohama
sapporo
nagano
nagasaki
sendai
kagoshima

From your list of destinations, i think one of the best base cities is Osaka. You can have a day trip to the following places: Kyoto, Nara, Himeji, and Kobe, and possibly mount Koya (Never been there so im not sure). The other places are kinda spread around.

I am a Japanese and I sometimes read about "base cities" from foreign travelers which seems to me very strange. If you have only 3 days to visit Kyoto, Nara, Osaka, Kobe and Koyasan, then Osaka as "base city" makes sense. However if you have 2 weeks to cover, you can stay Kyoto 5 nights, Koyasan for 1 nights, Nara for 2 nights etc. These sites are roughly 1 hours away each, so if you base Osaka and visit Kyoto 3 times, you will loose 4-6 hours of your travel time. Further, you must take "commuter trains" which are in general crowded and exhausting.

@Frog: I guess when people have that much time to spare, they rather waste some time on the train than have to bring their luggage to another hotel elsewhere. I've seen some major travel baggage before. Scary stuff.

@OP:
I would use Kanazawa as the base city for itself and Takayama.
Tokyo for itself and Nikko.
Matsumoto would be as a detour (no need to overnight).
I would choose Kyoto as the base city for the areas from Ise to Himeji. Mostly because you would probably be spending most of your time here.
Mt Koya is a place where you would have to stay a night.
Then another one or two at Hiroshima (cheaper) / Miyajima (more scenic). You can make a day trip to Fukuoka although I have no idea why people go all the way to Fukuoka but not see the rest of Kyushu.

I see you added in Hokkaido. Specifically noboribetsu. To go all the way there for this... is plain crazy. Sapporo is weird for the same reason.

Kamakura and Yokohama, day trips from Kyoto.

Shirakawa-go, either on itself or as a trip from Kanazawa.

Okinawa, Now i think you are just doing this for fun. That is like way over in the other side of Japan.

You also mentioned Matsumoto twice.

It is a pretty easy process. Look at a map and find the locations you are interested in. Group them all together and select a location in the center of those groups.

Kamakura and Yokohama, day trips from Kyoto.

I presume you meant to say Tokyo? Why on earth would you go there from Kyoto when you're also going to stay in Tokyo?

In terms of a location to stay at, my suggestion would be near stations that connect two different JR lines. Here is a link to the basic train page:

http://www.japan-guide.com/e/e2019.html

If you are looking to go places on the southern island of Kyushu, then Hakata Station in Fukuoka is probably the best location. It is the connection point of JR Kyushu and JR West. Hiroshima, Nagasaki, Kagoshima, Beppu, Huis Ten Bosche, are all less than two hours away, and can be done as a day trip. I use business class hotel rooms when I travel, and stay at the Route Inn in Hakata.

If you are looking at trips to Shikoku Island, I would stay in Okayama. Hiroshima, Osaka, Kyoto, Himeji, Takamatsu, and Tokushima are all within two hours. Matsue, Kochi, and Matsuyama are a little further away, but less than three hours.

For the Kansai area, The JR hub connection is Shin-Osaka Station. JR West and JR Central connect here.

For the Tokyo Area, many places are on the Yanamote Loop line. Here is a link:
http://www.japan-guide.com/e/e2370.html

Even though Tokyo is the hub connecting JR Central and JR East, the cost for a hotel near Tokyo station is very expensive, so I don't stay there. I usually stay in Nippori Station, which is on the Yamanote loop. I stay here because I usually go to Fabric Taon in Nippori, and because it also has direct trains to Narita Airport. My strong suggestion for general tourism would be near Shinjuku Station. There are many passes to places from Shinjuku, such as Kamakura, Hakone, Ito, and the Fuji Five Lakes. There is also a JR Limited Express train that goes to Nikko from Shinjuku. More Links:
http://www.japan-guide.com/e/e2358_003.html
http://www.japan-guide.com/e/e2358_008.html
http://www.japan-guide.com/e/e2358_014.html
http://www.japan-guide.com/e/e2358_007.html
http://www.japan-guide.com/e/e6905.html

For the Tohoku region, I would probably take Sendai(southern choice) or Morioka (Northern choice). In the future, I am planning a summer trip to see the big three festival in Tohoku in August. I will probably stay in Morioka first for a while, and then switch to Sendai.

I would probably base myself in Sapporo in Hokkaido.

Is this what you were looking for?