I have to second a bunch of the things Animeniax said, particularly the bath houses / hot springs, ramen + gyoza, and the nice, high-end dinner (I'd say traditional Japanese over steak, but that's just me). I have no love for the capsules, and would say, if you want to try sleeping in a weird place, that you do an internet cafe.

First thing's first. It's nice to lose yourself in fantasies, but you need to budget and plan. ("Those who fail to plan...") Traveling is a tiring thing, and I can't imagine you want to spend half the time on trains/planes, building up a huge cost, just to be too tired to enjoy what you see. Get a list in mind and be ready to compromise for feasibility.

AVOID OBON, AVOID GOLDEN WEEK, DONT GET RIPPED
it's already going to suck paying for this with the Yen beating up on the Dollar, and then you will be paying much more for hotels and transportation (Get that rail pass) and competing with all the other travelers for the few good deals, not to mention the crowds.

I would recommend:
Tokyo, particularly Meiji Jingu (and right near Cosplayer Corner and the super trendy Harajuku), Asakusa, Shibuya (to glimpse the night clubs / popular scene). If you want a major club, try Ageha out in Shin Kiba.
Around Tokyo there are lots of things to do for one day trips. Nikko, Yokohama are the top two I'd suggest. Natural beauty and urban delight, respectively

Osaka / Kyoto
For your base of operations in the south / old part, you can use either of these two. Kyoto has lots of temples and traditional stuff(daytime), but if you're feeling more Big City (nightlife), Osaka is better. No matter what, get to the big forest/river area outside of Kyoto, and see the temples there.
Not so much to do in Osaka as far as culture goes.

Hit up Nara for a one day trip from Osaka / Kyoto.
Hit up Himeji for the castle, then check out Kobe for afternoon / night. Some nice shopping, a decent China Town, and good food.

The rest:
hokkaido is beautiful if you like the outdoors, and it will be nice and cool during the summer while you sweat like hell in the rest of Japan. But it is a bit out of the way, and, really, unless you like hiking and the outdoors, not recommended for a short trip. Sapporo is considered the biggest city up there, but unless it's the time of year they have the Beer Gardens open, not very good at all (the cultural village nearby it is pretty cool though)
Biei / Furano are beautiful, but very simple. Outdoors
Hakodate is in the South of Hokkaido, and it's the place I liked the best. You can do some hiking in the mountain area, and it's just a really quaint kind of town.

Don't know much about the southern islands, so can't really say.

Food: Mandatory stuff is Kaiten Sushi (revolving sushi bar), Ramen, Okonomiyaki. You'll probably be finding yourself at the cheap 24/7 places too. Eat from a convenince store at least once. I also recommend Takoyaki while in Osaka/Kyoto, and you should absolutely hit up Sukiyaki or Yakiniku for a nice dinner too.

have a good trip!