Stay at a box hotel
If you like walking and market areas, you could also check out Ameyoko while doing the above.
This covers part of the trip from Ueno to Akihabara. I did this walk when I was in Japan, and had quite a good day.
I’m about as geeky as they come and the appeal of Akihabara was lost on me. There were a bunch of electronics stores and once in a while you’d see a woman wearing a maid’s uniform handing out flyers (or whatever). Likewise, the area where they sell the fake plastic food wasn’t that interesting, just a bunch of restaurant supply stores with one or two selling something slightly unusual. YMMV, of course.
Also, while there are excellent restaurants in Tokyo, the strategy my wife and I used of picking the closest likely-seeming restaurant whenever my wife got hungry produced mixed results. A little pre-planning of meals would probably go a long way.
This is an interesting point of view which is exactly opposite to mine. 
I love Japanese castles, having visited many of them, as well as many more of the sites where unfortunately where there used to be ones. (The Tokugawa bokufu (shogun) government made many local leaders destroy theirs, and the Meiji government which was formed in the late 19th century destroyed many others. There are only a few historical castles left.)
I would give the exact opposite advice. Skip the ugly concrete reconstructed Osaka monstrosity(!) (IMHO) and visit the actual wood-built, historical Himeji-jo. There is a wonderful museum next the the castle which goes into great detail about Japanese castles.
It really depends on what you like.
In the pre-cell phone days it was said that if you really hated someone, arrange to meet them in the Ikubukuro station.
It sounds like you’ll be a couple of weeks early for cherry blossoms. That was not something I would have ever planned a trip around, but I just happened to be there the first week of April last year, and it was pretty impressive. They made a picnic on the Himeji grounds quite the cultural experience; for that matter they turned Peace Park in Hiroshima into something magical.
Try out conveyer belt sushi. And yeah, stay in a box hotel. And I’ve heard there’s this weird robot restraunt. Giant Fembots Dance With Dinosaurs in the Weirdest Show on Earth | WIRED Conveyor belt sushi - Wikipedia
I’d suggest getting to know the train system. It can be very complex and intimidating for the uninitiated but it’s the only way to really get around. Learn to recognize the kanji for the trains lines and the stops you need to arrive at.
Japan is my favorite place in the world, and I love Tokyo. Take I think it’s the JR line that runs in a circle around the city. One hour for a full circuit, and it gives you a good view of the place. I know there are other threads about what to do in Tokyo that I’ve contributed to. Try looking those up. Included are some pretty good hop-on/hop-off tours. And do hit Yokohama for a day – about half an hour from Tokyo Station IIRC.
Nearly everything about Japanese train systems—even small, private lines like the Shodan Monorail or Enoden Railway—is also in Roman characters these days, and most station announcements on JR and the subways are also made in English. Even bus headsigns will alternate Kanji with Romanji.
As for riding the Yamanote Line in a circle around the city, that’s not a terrible idea, but the seating is all along the windows, facing into the car, IRT style. So it’s difficult to see out very well, especially if the train has standees—which it nearly always has. I prefer to just hop on a random crosstown bus whose terminus is some place I recognize.
Tokyo is trying to make things easy for the upcoming Olympics. The subway system is extensive and confusing at first, especially since two companies own different lines. You can use both for a daily ticket about ten dollars a day. You can save money by getting a train pass or longer subway pass, and cheaper still if you buy it before going to Japan (see JR East train pass if going to many places). All things considered, given that Japan has 40 million people and the subway moves almost 9 million people a day, it is very well organized. Make sure to carry a pocket map of the subway from any travel book or omnipresent tourist magazines.
Subway stops are numbered, that part is easy and you don’t need to know Kanji. At busy times, however, many subway trains are express and stop off at every fourth stop, for example. Do pay attention to whether a train is local, express or in-between and find the poster at each subway showing the time (and they are always on time) and where it stops.
It’s more than two companies running the line, isn’t it? Could be up to five.
try to see some puroesu <sp> I’m told a new japan pro wrestling card is exciting even for non fans because of the showmanship …
Lots of suggestions, almost all good. Research the ones that look appealing to you. Some updates (I live in the Tokyo area currently):
The fish market (Tsukuji) is shut down right now because they’re moving to new facilities. It’s taking a while because there’s some controversy about the new site; problems with construction and prior contamination. Neither site is open to the public and won’t be for months.
Himeji castle just went through a restoration. Everything was redone in historical styles, some safety reinforcement, etc. I haven’t seen it in person, but apparently it was well done. Matsumoto in Nagano Prefecture is one of the other remaining original structures. There are only about 4 on Honshu (the main island) out of the 12 total in all the islands that are not ferroconcrete reconstructions. Those two are the best.
The Robot Show is fun. It’s primo modern-Japanese gaijin-friendly weirdness. It’s like Akihabara and Shibuya mated in a video game and the Masked Rider (Kamen Raidā) was the midwife. Plus dancing and taiko. Most of the patrons will be foreigners (more than 2/3 in the one I attended). It’s loud. Bring earplugs. Don’t buy the food, just the beer. If one of you likes girls and the other is prone to jealousy, probably shouldn’t go. The performers are gorgeous and often scantily-clad.
If you’re going to travel by rail, look into getting a JR Rail pass. You can only apply for those from overseas before you come. The benefit is a fixed price for as much as you can ride. Take a look at your overall itinerary and see if it’s appropriate. It can be used for local rides too. The drawback is that it’s not usable on non-JR lines. There are many independent metro and local lines that connect in the major cities. JR will generally get you there too, but sometimes not as directly or shortly as alternatives.
Don’t count on swapping your SIM for a pre-paid. Japan is still not particularly friendly to small carriers, and the major 3 don’t cater well to non-residents. You’ll probably have to use roaming. There are few wi-fi spots too. Do some research, though. Visitors might know something I don’t. Data access can make your life much, much easier.
The Harajuku crowd has moved. Too many tourists. The Rockabilly guys were still there with amazing pompadours and duck-ass hairdos on Sundays.
Good places for souvenirs are around in Harajuku, down the street from the park. Akasaka near the shrine. Ginza, in some places; small shops change often.
Depending on what you’re interested in, you’re probably spoiled for choice. Don’t plan too much. Focus on your interests mainly, fit in other stuff based on proximity to those.
Traveling takes longer than you’d think. I’m only about 20 km from Tokyo station, which would be a 15 minute drive most places in the US. Trains always run on time, but it’ll take you at least 40 minutes to cover that kind of distance, plus getting to the station and wait time; figure an hour minimum one-way for that trip.