Great how you prepare your trip Kowalp.
Day 1: I am happy you consider the Tsukiji Fish Market. Try to go into the inner market first. Watch out for the carts and don't stay too long in the same position. But you will be surprised by the crazy activity and the dozens of small shops. Then you can go to the outer market. I tried out several restaurants in and around Tsukiji. You can p.m. me if you want recommendations. Today for example I had lunch and paid only 2400 yen for two (we had each 10-13 sushi), and the quality was exquisite. After breakfast/lunch, you can go back to the inner market, when the activity is over and when it is desolate... Such an interesting contrast. You see some people cleaning their material, leftover fish here and there, a rat sometimes,... I am happy the fisk market hasn't moved yet to Toyosu.
In my opinion, both Tokyo International Forum and Imperial Palace and East Garden, are not very interesting. The Imperial Palace, you cannot see and the garden itself is very plain and even boring, with relatively big paths.
Instead, I would recommend you to go to Hamarikyu garden (300 yen), close to Tsukiji. From the garden, you can see the skyscrapers from Shinbashi, which is again a nice contrast with the garden. You can take the boat to Asakusa for example. There are some duck hunting ponds.
Another option is to wander through Ginza for shopping and for architecture (De Beers, Mikimoto, Yamaha, Tokyu Plaza and Kiriko lounge, the Nissan Gallery,...).
Day 2: Since you are in the neighbourhood, I recommend you to walk through Omotesando and look up for the architecture. There is an article here on TokyoCheapo about an architecture walk. There are many interesting buildings like the Prada shop, the Hugo Boss hourglass,... You seem to have forgotten Takeshita Dori in your list. I am not really a fan of Roppongi, so in my opinion not necessary.
Day 3: I would only go to Ueno Park during the hanami. Same for Yoyogi park. Other parks you can go to are Rikugien and Kiyosumi Teien. Both are very traditional Japanese gardens. In Akihabara you might make a stop at M's Pop Life adult department store, but look up first what it exactly is.
Day 5: Meiji Shrine is close to Takeshita, Omotesando,... So it would be better on day 2 in your planning. I was quite disappointed by Meiji shrine, although I must say I visited it after I went to Kyoto and where I saw beautiful shrines. I think Yasukuni shrine is more interesting in Tokyo.
Since you are staying a long time in Tokyo, I would make 1 or 2 day trips:
- if you like hiking: Nokogiriyama (or Takaosan, Tsukubasan, Mitake with rock garden,...)
- Enoshima (where I saw the most beautiful sunset behind Fujisan, so preferably on a clear day!)
- Nikko, although i haven't been myself
You can also go to the Daikanyama - Nakameguro neighbourhood, which is pretty nice. The walk along the river is magical during cherry blossom season.